A074207 Numbers k such that the sum of the first k primes divides k!.

11, 17, 23, 37, 40, 49, 50, 52, 53, 56, 77, 79, 80, 84, 87, 88, 91, 98, 103, 111, 112, 113, 115, 119, 121, 127, 128, 131, 139, 149, 151, 153, 157, 163, 172, 173, 179, 188, 213, 217, 230, 231, 237, 240, 245, 247, 253, 269, 270, 271, 275, 283, 285, 295, 297, 299

Offset

1,1

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Example

11! / Sum_{i=1,...,11} Prime[i] = 249480, so 11 is a term of the sequence.

Mathematica

s = 0; p = 1; r = {}; For[i = 1, i <= 500, i++, q = Prime[i]; s = s + q; p = p * i; If[Mod[p, s] == 0, r = Append[r, i]]]; r
With[{nn=300}, {sfnp=Accumulate[Prime[Range[nn]]]}, Select[Thread[{Range[nn], sfnp}], Mod[#[[1]]!, #[[2]]]==0&]][[;; , 1]] (* Harvey P. Dale, Mar 23 2026 *)

Crossrefs

Sequence in context: A219602 A242260 A076812 * A063638 A141250 A316188

Adjacent sequences: A074204 A074205 A074206 * A074208 A074209 A074210

Keyword

nonn

Author

Joseph L. Pe, Sep 17 2002

Status

approved