This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A219546 #17 Dec 21 2020 02:04:02
%S A219546 5,13,23,31,37,41,43,47,53,59,61,71,79,101,103,107,109,127,137,149,
%T A219546 157,163,173,179,181,191,197,199,211,223,229,241,251,257,263,271,277,
%U A219546 283,293,311,317,337,349,353,359,367,383,397,401,409,419,421,431,439,461
%N A219546 Schenker primes.
%C A219546 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.
%C A219546 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.
%H A219546 Vaclav Kotesovec, <a href="/A219546/b219546.txt">Table of n, a(n) for n = 1..783</a>
%H A219546 T. Amdeberhan, D. Callan, and V. Moll, <a href="http://dauns.math.tulane.edu/~vhm/papers_html/schenker.pdf">p-adic analysis and combinatorics of truncated exponential sums</a>, preprint, 2012.
%H A219546 T. Amdeberhan, D. Callan and V. Moll, <a href="http://www.emis.de/journals/INTEGERS/papers/n21/n21.Abstract.html">Valuations and combinatorics of truncated exponential sums</a>, INTEGERS 13 (2013), #A21.
%e A219546 5 is a Schenker prime because 2 < 5 and 5 divides A063170(2) = 10.
%e A219546 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.
%t A219546 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 *)
%Y A219546 Cf. A063170.
%K A219546 nonn
%O A219546 1,1
%A A219546 _Jonathan Sondow_, Nov 22 2012
%E A219546 More terms from _Vaclav Kotesovec_, Nov 30 2017