A366489 -id:A366489 - 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

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

A366491 a(n) = (n^19 - n)/19.

Original entry on oeis.org

0, 0, 27594, 61171656, 14467258260, 1003867701480, 32071565263710, 599941851861744, 7585009898729256, 71097458824894320, 526315789473684210, 3218899497284976120, 16814736808980154044, 76943173177655058456, 314542313628890231430, 1166756747396368729440, 3976729669784964390480, 12582759772902701307744, 37275544492386193492506, 104127350297911241532840, 275941052631578947368420

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 (20, -190, 1140, -4845, 15504, -38760, 77520, -125970, 167960, -184756, 167960, -125970, 77520, -38760, 15504, -4845, 1140, -190, 20, -1).

Cf. A000217, A007290, A110936, A208536, A208537, A366488, A366489, A366490.

A366491[n_]:=(n^19-n)/19;Array[A366491,30,0] (* Paolo Xausa, Nov 15 2023 *)

a(n) = 0 (mod 42), with 42 = A110936(primepi(19)). - Hugo Pfoertner, Nov 14 2023

cp's OEIS Frontend

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

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

Formula

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

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

Formula

A366491 a(n) = (n^19 - n)/19.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

Formula