A067008 Numbers k such that Sum_{j=1..k} A008472(j) divides k!.

2, 5, 7, 10, 13, 16, 19, 20, 31, 34, 37, 40, 41, 44, 46, 48, 51, 53, 55, 56, 62, 64, 65, 67, 68, 69, 73, 74, 76, 79, 81, 82, 83, 84, 85, 86, 87, 89, 95, 96, 97, 99, 100, 101, 106, 107, 108, 109, 111, 112, 115, 119, 121, 122, 123, 124, 133, 134, 135, 136, 137, 138, 143

Offset

1,1

Links

Giovanni Resta, Table of n, a(n) for n = 1..10000 (first 4114 terms from Daniel Starodubtsev)

Formula

a(n) seems to be asymptotic to c*n with c=2.3.....

Mathematica

tot[n_] := tot[n] = If[n < 2, 0, tot[n - 1] + Plus @@ FactorInteger[n][[;; , 1]]]; ef[n_, p_] := Block[{c=0, m=n}, While[m > 0, m = Floor[m/p]; c += m]; c]; ok[n_] := n > 1 && AllTrue[ FactorInteger@ tot@n, #[[1]] <= n && ef[n, #[[1]]] >= #[[2]] &]; Select[ Range@ 1000, ok] (* Giovanni Resta, Dec 13 2019 *)

Prog

(PARI) for (j=2, 143, if(!(j!%sum(k=1, j, vecsum(factor(k)[, 1]))), print1(j, ", "))) \\ Hugo Pfoertner, Dec 13 2019

Crossrefs

Cf. A008472.

Sequence in context: A364005 A081838 A057347 * A376959 A189757 A094065

Adjacent sequences: A067005 A067006 A067007 * A067009 A067010 A067011

Keyword

nonn

Author

Benoit Cloitre, Oct 03 2002

Status

approved