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

1,1

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

Links

Table of n, a(n) for n=1..21.

Example

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).

Mathematica

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

Prog

(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

Crossrefs

Cf. A000005, A061358.

Sequence in context: A274189 A275194 A341173 * A074757 A211710 A039327

Adjacent sequences: A352784 A352785 A352786 * A352788 A352789 A352790

Keyword

nonn,more

Author

Wesley Ivan Hurt, Apr 02 2022

Status

approved