A213650 -id:A213650 - cp's OEIS frontend

A213734 Primes in A213650.

3, 7, 59, 137, 277, 313, 499, 563, 619, 719, 787, 797, 919, 937, 971, 1013, 1217, 1283, 1373, 1409, 1439, 1451, 1621, 1747, 1789, 2207, 2237, 2267, 2393, 2417, 2441, 2591, 2707, 2797, 2801, 2939, 2999, 3251, 3529, 3769, 3847, 4201, 4441, 4447, 4597, 4643, 4721

Offset: 1

Michel Lagneau, Jun 19 2012

nonn

Primes p such that the sum of the first p primes is semiprime.

			7 is in the sequence because the sum of the first 7 primes is 2 + 3 + 5 + 7 + 11 + 13 + 17 = 58 = 2*29, which is semiprime.

Cf. A213650.

with(numtheory): for n from 1 to 10000 do:s:=sum(‘ithprime(k)’, ’k’=1..n):if bigomega(s)=2 and type(n,prime)=true then printf(`%d, `, n):else fi:od:

Select[Flatten[Position[If[PrimeOmega[#]==2,1,0]&/@Accumulate[ Prime[ Range[ 5000]]],1]],PrimeQ] (* Harvey P. Dale, Jan 27 2022 *)

isok(n) = isprime(n) && bigomega(vecsum(primes(n))) == 2; \\ Michel Marcus, Sep 18 2017

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

Original entry on oeis.org

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

Jonathan Vos Post, Jun 19 2012

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

			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.

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

Cf. A007504, A014612, A213650.

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 *)

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

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

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A213734 Primes in A213650.

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