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A219546 Schenker primes. 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

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.

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.

EXAMPLE

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.

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 *)

CROSSREFS

Cf. A063170.

Sequence in context: A006353 A155142 A155552 * A143988 A129806 A125830

Adjacent sequences:  A219543 A219544 A219545 * A219547 A219548 A219549

KEYWORD

nonn

AUTHOR

Jonathan Sondow, Nov 22 2012

EXTENSIONS

More terms from Vaclav Kotesovec, Nov 30 2017

STATUS

approved

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Last modified June 15 11:22 EDT 2021. Contains 345048 sequences. (Running on oeis4.)