A366491 -id:A366491 - cp's OEIS frontend

A366488 a(n) = (n^11 - n)/11.

0, 0, 186, 16104, 381300, 4438920, 32981550, 179756976, 780903144, 2852823600, 9090909090, 25937424600, 67546215516, 162923672184, 368142288150, 786341441760, 1599289640400, 3115626937056, 5842582734474, 10590023536200, 18618181818180, 31843409140200, 53119845582846, 86619068901264, 138334649379000, 216744162819600

Offset: 0

N. J. A. Sloane, Nov 13 2023

If p is a prime, (n^p-n)/p is an integer by Fermat's Little Theorem. For p = 2, 3, 5, 7, ..., this gives A000217, A007290, A208536, A208537, this sequence, A366489, A366490, A366491.

Stefano Spezia, Table of n, a(n) for n = 0..10000
Jack Jeffries, Differentiating by prime numbers, Notices Amer. Math. Soc., 70:11 (2023), 1772-1779.
Index entries for linear recurrences with constant coefficients, signature (12,-66,220,-495,792,-924,792,-495,220,-66,12,-1).

Cf. A000217, A007290, A208536, A208537, A366489, A366490, A366491.

A366488[n_]:=(n^11-n)/11;Array[A366488,30,0] (* Paolo Xausa, Nov 14 2023 *)
LinearRecurrence[{12,-66,220,-495,792,-924,792,-495,220,-66,12,-1},{0,0,186,16104,381300,4438920,32981550,179756976,780903144,2852823600,9090909090,25937424600},30] (* Harvey P. Dale, Aug 03 2025 *)

a(n) == 0 (mod 6). - Hugo Pfoertner, Nov 14 2023

A366489 a(n) = (n^13 - n)/13.

Original entry on oeis.org

0, 0, 630, 122640, 5162220, 93900240, 1004668770, 7453000800, 42288908760, 195528140640, 769230769230, 2655593241840, 8230246567620, 23298085122480, 61054982558010, 149707312950720, 346430740566960, 761890617915840, 1601766528128550, 3234844881712080

Offset: 0

N. J. A. Sloane, Nov 13 2023

See A366488 for further information.

Stefano Spezia, Table of n, a(n) for n = 0..10000
Jack Jeffries, Differentiating by prime numbers, Notices Amer. Math. Soc., 70:11 (2023), 1772-1779.
Index entries for linear recurrences with constant coefficients, signature (14,-91,364,-1001,2002,-3003,3432,-3003,2002,-1001,364,-91,14,-1).

Cf. A000217, A007290, A208536, A208537, A366488, A366490, A366491.

A366489[n_]:=(n^13-n)/13; Array[A366489,30,0] (* Paolo Xausa, Nov 14 2023 *)

a(n) == 0 (mod 210). - Hugo Pfoertner, Nov 14 2023

A366490 a(n) = (n^17 - n)/17.

Original entry on oeis.org

0, 0, 7710, 7596480, 1010580540, 44878791360, 995685849690, 13684147881600, 132458812569720, 981010688215680, 5882352941176470, 29732178147017280, 130506535690613940, 508847995257725760, 1793608631137129170, 5795654431511374080, 17361641481138401520

Offset: 0

N. J. A. Sloane, Nov 13 2023

See A366488 for further information.

Stefano Spezia, Table of n, a(n) for n = 0..10000
Jack Jeffries, Differentiating by prime numbers, Notices Amer. Math. Soc., 70:11 (2023), 1772-1779.
Index entries for linear recurrences with constant coefficients, signature (18,-153,816,-3060,8568,-18564,31824,-43758,48620,-43758,31824,-18564,8568, -3060,816,-153,18,-1).

Cf. A000217, A007290, A110936, A208536, A208537, A366488, A366489, A366491.

A366490[n_]:=(n^17-n)/17;Array[A366490,30,0] (* Paolo Xausa, Nov 14 2023 *)

a(n) == 0 (mod 30), with 30 = A110936(primepi(17)). - Hugo Pfoertner, Nov 14 2023

cp's OEIS Frontend

A366488 a(n) = (n^11 - n)/11.

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A366489 a(n) = (n^13 - n)/13.

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A366490 a(n) = (n^17 - n)/17.

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