A219546 Schenker primes.

5, 13, 23, 31, 37, 41, 43, 47, 53, 59, 61, 71, 79, 101, 103, 107, 109, 127, 137, 149, 157, 163, 173, 179, 181, 191, 197, 199, 211, 223, 229, 241, 251, 257, 263, 271, 277, 283, 293, 311, 317, 337, 349, 353, 359, 367, 383, 397, 401, 409, 419, 421, 431, 439, 461

Offset: 1

Author

Jonathan Sondow, Nov 22 2012

Keywords

• nonn

Comments

Amdeberhan, Callan, and Moll (2012) call a prime p a Schenker prime if p divides A063170(r) (the r-th Schenker sum with n-th term) for some r < p.

For any non-Schenker prime p, Amdeberhan, Callan, and Moll (2012) give a formula for the p-adic valuation of any Schenker sum with n-th term.

Examples

			5 is a Schenker prime because 2 < 5 and 5 divides A063170(2) = 10.
17 is not a Schenker prime because 17 is not a factor of A063170(1) = 2, or of A063170(2) = 10, . . . , or of A063170(16) = 105224992014096760832.
		

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 1..783
• T. Amdeberhan, D. Callan, and V. Moll, p-adic analysis and combinatorics of truncated exponential sums, preprint, 2012.
• T. Amdeberhan, D. Callan and V. Moll, Valuations and combinatorics of truncated exponential sums, INTEGERS 13 (2013), #A21.

Crossrefs

Cf. A063170.

Programs

Mathematica

pmax = 300; A063170 = Table[n!*Sum[n^k/k!, {k, 0, n}], {n, 1, pmax}]; Rest[Select[Table[If[PrimeQ[j] && SelectFirst[Range[j], Divisible[A063170[[#]], j] &] != j, j, 0], {j, 1, pmax}], # != 0 &]] (* Vaclav Kotesovec, Nov 30 2017 *)

Extensions

More terms from Vaclav Kotesovec, Nov 30 2017