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A213741 Numbers n such that the sum of the first n primes is divisible by exactly 3 prime powers (not including 1). 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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified December 1 11:38 EST 2021. Contains 349429 sequences. (Running on oeis4.)