A352787 Numbers with as many divisors as Goldbach partitions.

34, 46, 58, 102, 116, 122, 138, 150, 154, 162, 172, 184, 190, 196, 212, 228, 264, 266, 296, 304, 332

Offset: 1

Author

Wesley Ivan Hurt, Apr 02 2022

Keywords

• nonn
• more

Comments

If it exists, a(22) > 7*10^5. - Ivan N. Ianakiev, Apr 11 2022

Numbers k such that A000005(k) = A061358(k). - Michel Marcus, Apr 12 2022

Examples

			122 is in the sequence since it has 4 divisors {1,2,61,122} and 4 Goldbach partitions (13,109), (19,103), (43,79), (61,61).
		

Crossrefs

Cf. A000005, A061358.

Programs

Mathematica

Select[Range[332],DivisorSigma[0,#]==Length[Select[#-Prime[Range[PrimePi[#/2]]], PrimeQ]]&] (* Ivan N. Ianakiev, Apr 11 2022 *)

PARI

nbgp(n) = my(s); forprime(q=2, n\2, s+=isprime(n-q)); s; \\ A061358
isok(k) = numdiv(k) == nbgp(k); \\ Michel Marcus, Apr 12 2022