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

Author

Benoit Cloitre, Oct 03 2002

Keywords

• nonn

Links

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

Crossrefs

Cf. A008472.

Programs

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 *)

PARI

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

Formula

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