鹿児島大学リポジトリ

(1)

CORRIGENDA

著者

ORIGUCHI Tadashi, KIRIYAMA Hiroshi, MATSUOKA

Yoshio

journal or

publication title

鹿児島大学理学部紀要. 数学・物理学・化学

volume

22 page range

133-134

別言語のタイトル

「自然数のべき和 Sp(n)=Σn k=1 kp FOR

p=62(1)99の公式について」の訂正

URL

http://hdl.handle.net/10232/6463

(2)

CORRIGENDA

著者

ORIGUCHI Tadashi, KIRIYAMA Hiroshi, MATSUOKA

Yoshio

journal or

publication title

鹿児島大学理学部紀要. 数学・物理学・化学

volume

22 page range

133-134

別言語のタイトル

「自然数のべき和 Sp(n)=Σn k=1 kp FOR

p=62(1)99の公式について」の訂正

URL

http://hdl.handle.net/10232/00000499

(3)

Rep. Fac. Sci. Kagoshima Univ., (Math., Phys. & Chem.) No. 22. p. 133-134, 1989.

CORRIGENDA

Tadashi Origuchi* Hiroshi Kiriyama* and Yoshio Matsuoka** (Received 10 September, 1989)

〟

I. A table of the explicit formulas for the sums of powers Sp(ri)-k茎lk♪ forp-l (1) 61, these Rep. No. 20 (Dec, 1987), ll-31.

On p. 14, the both members of the formula representing S23(n) are divisible by Thus we should read

72肪23'(ォ) - n2(n+l)2(30n20 + 300ォ19 + 750w18 - 1800ォ17 - 7776w16 + 17352ォ15 + 69212m14 - 1 55776m13 - 4 93131m12 + ll 42038mll + 26 66455m10 - 64 74948w9 - 102 50315ォ8 + 269 75578ォ7 + 249 43119ォ6 - 768 61816ォ5 - 277 01758m4 + 1322 65332m3 - 148 61886m2 - 1025 41560m + 512 70780) instead of 娼23(n) - n2(n+lf(690n20 + 6900ra19 + 17250ォ18 -... - 23584 55880ォ+ 11792 27940).

Similarly, on pp. 18-19, the both sides of the formula expressing S4i(n) are divisible by 41. Therefore we should read

13860S4i(ォ) -ォ2(ォ+l)2(330ォ38 + 6270ォ37 + 34485ォ36 - 75240n35 - ll 15235W34 + 23 05710w33 + 377 20705m32 - 777 47120m31 - 11805 58500m30 + 24388 64120m29 + 3 30889 04585ォ28 - 6 86166 73290m27 - 81 95121 12573m26 + 170 76408 98436m25 + 1775 54185 11501m24 - 3721 84779 21438m23 - 33301 97740 43847n22 + 70325 80260 09132n21 + 5 34274 23573 67833w20 - ll 38874 27407 44798ォ19 - 72 27892 32390 91857ォ18 + 155 94658 92189 28512n17 + 810 26785 04847 45933ォ16 - 1776 48229 01884 20378サ15 - 7362 95473 79024 36727w14 + 16502 39176 59932 93832m13 + 52687 78517 08935 54393m12 - 1 21877 96210 77804 02618ォn - 2 85118 80770 40981 89037/slO + 6 92115 57751 59767 80692ォ9 + 10 96163 68766 10469 24253ォ8 - 28 84442 95283 80706 29198n' - 26 67400 66432 00690 89360ォ6 + 82 19244 28147 82088 07918m5 + 29 62385

* Kagoshima High School

(4)

134 Corrigenda ● 71510 57459 07749ォ4 - 141 44015 71168 97006 23416w3 + 15 89270 76741 94187 48637ォ2 + 109 65474 17685 08631 26142w - 54 82737 08842 54315 63071 instead of 5 68260S4i(w)-ォ2(サ+l)2(13530ォ38 + 2 57070w37 + 14 13885ォ36 -... + 4495 84441 25088 53881 71822m - 2247 92220 62544 26940 85911). n

II. A table of the explicit formulas for the sums of powers Sp(n)-蔓1k♪ for 6-1 (1) 61, II, these Rep. No. 21 (Feb., 1989), 49-64.

On p. 50, line 6打om the bottom, we should read Mr. Shigeshi Shirasaka for Shigeru Shirasaka.

On p. 55, co汀esponding to the reduction mentioned in I above, we should read

72(娼23(ォ)-m2(30m10 - 600m9 + 7524m8 - 72160m7 + 5 44599m6 - 31 82232m5 + 139 00616m4 - 430 94016m3 + 876 79674m2 - 1025 41560m + 512 70780)

br

娼23(ォ)-w2(690m10 - 13800w9 + 1 73052m8 - - - 23584 55880m + 11792 27940.

S血ilarly, on p. 58 we should read

娼4i(ォ)-m2(330m19 - 21945m18 + 9 63270m17 - 350 85875m16 + 11196 08820m15 - 3 16053 73965m14 + 78 68051 13512m13 - 1714 88180 61540m12 + 32421 78909 21078m11 - 5 25912 23202 65099mlO + 72 25369 86279 32094m9 - 827 97178 04626 94439m8 + 7768 33044 83182 16590m7 - 58325 32903 97168 20026m6 + 3 40407 74788 81408 51248m5 - 14 86584 19698 23741 09528m4 + 46 08391 10717 31881 31594m3 - 93 76203 40943 14443 77505m2 + 109 65474 17685 08631 26142m - 54 82737 08842 54315 63071) for 5 68260S4i(ォ)-m2(13530m19 - 8 99745m18 + 394 94070m17 - - + 4495 84441 25088 53881 71822w - 2247 92220 62544 26940 85911).