A213741 Numbers n such that the sum of the first n primes is divisible by exactly 3 prime powers (not including 1).

5, 13, 20, 23, 24, 35, 39, 41, 42, 43, 47, 50, 56, 61, 62, 63, 67, 68, 69, 70, 73, 76, 78, 81, 86, 90, 98, 112, 123, 126, 128, 134, 143, 145, 147, 160, 165, 166, 172, 176, 180, 182, 186, 189, 191, 193, 196, 197, 200, 215, 220, 222, 223, 225, 227, 229, 238

Offset

1,1

Comments

This is to "triprimes" or "3-almost primes" A014612 as A213650 is to semiprimes A001358.

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Formula

{n such that A007504(n) is included in A014612.}

Example

a(1) = 5 because the sum of first 5 primes is 28 = 2^2 * 7 which has exactly three prime power factors (not including 1).
a(2) = 13 because the sum of first 13 primes is 238  =  2 * 7 * 17  which has exactly three prime power factors (not including 1).
a(3) = 20 because the sum of first 20 primes is 639 = 3^2 * 71.

Mathematica

ps = 0; t = {}; Do[ps = ps + Prime[n]; If[Total[Transpose[FactorInteger[ps]][[2]]] == 3, AppendTo[t, n]], {n, 300}]; t (* T. D. Noe, Jun 27 2012 *)

Prog

(PARI) list(lim)=my(v=List(), k, s); forprime(p=2, prime(lim\1), k++; if(bigomega(s+=p)==3, listput(v, k))); Vec(v) \\ Charles R Greathouse IV, Feb 05 2017

Crossrefs

Cf. A007504, A014612, A213650.

Sequence in context: A265814 A087714 A055045 * A184825 A190372 A184837

Adjacent sequences: A213738 A213739 A213740 * A213742 A213743 A213744

Keyword

nonn,easy

Author

Jonathan Vos Post, Jun 19 2012

Status

approved