A108048 -id:A108048 - cp's OEIS frontend

A108496 a(n) = (n^43 - n)/42.

0, 0, 209430786243, 7815642080822311372, 1842172677508006361457030, 27068294695622864223661876860, 68747114771196346634599779308105, 51995580380757061883555053636996008

Offset: 0

Henry Bottomley, Jun 06 2005

nonn

Also integer sequences for (n^2-n)/1 (A002378 offset), (n^3-n)/2 (A027480 offset), (n^7-n)/6 (A108495) and (n^1807-n)/1806.

			a(2) = (2^43 - 2)/42 = 8796093022206/42 = 209430786243.

Vincenzo Librandi, Table of n, a(n) for n = 0..1000
D. Zagier, Problems posed at the St Andrews Colloquium, 1996.

Cf. A014117, A108497, A108499.

[(n^43-n)/42: n in [0..20]]; // Vincenzo Librandi, May 02 2011

Table[(n^43-n)/42,{n,0,10}] (* Harvey P. Dale, Jan 31 2022 *)

a(n) = (n-1)*A108048(n).

A108498 Triangle read by rows: T(n,k) = sum_i{1<=i<=n} k^i mod n, showing 1<=k<=n.

Original entry on oeis.org

0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 2, 3, 4, 0, 0, 0, 0, 0, 0, 0, 0, 2, 3, 4, 5, 6, 0, 0, 6, 0, 4, 0, 2, 0, 0, 0, 5, 3, 0, 2, 6, 0, 8, 0, 0, 6, 2, 0, 0, 0, 6, 2, 0, 0, 0, 2, 3, 4, 5, 6, 7, 8, 9, 10, 0, 0, 6, 0, 0, 0, 6, 0, 0, 0, 6, 0, 0, 0, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 0, 0, 6, 12, 6, 2, 0, 0, 0, 6, 12, 6, 2

Offset: 1

Henry Bottomley, Jun 06 2005

			Rows start: 0; 0,0; 0,2,0; 0,2,0,0; 0,2,3,4,0; 0,0,0,0,0,0; 0,2,3,4,5,6,0; etc.
T(7,3) = 3+9+27+81+243+729+2187 mod 7 = 3279 mod 7 = 3.

Cf. A014117, A059721, A108048, A108497, A108499.

T(n, k+n)=T(n, k). T(n, 0)=T(n, 1)=T(n, n)=T(1, k)=T(2, k)=T(6, k)=T(42, k)=T(1806, k)=0. T(p, k)=k for p prime and 1

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cp's OEIS Frontend

A108496 a(n) = (n^43 - n)/42.

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