A316525 Numbers whose average of prime factors is prime.

2, 3, 4, 5, 7, 8, 9, 11, 13, 16, 17, 19, 20, 21, 23, 25, 27, 29, 31, 32, 33, 37, 41, 43, 44, 47, 49, 53, 57, 59, 60, 61, 64, 67, 68, 69, 71, 73, 79, 81, 83, 85, 89, 93, 97, 101, 103, 105, 107, 109, 112, 113, 116, 121, 125, 127, 128, 129, 131, 133, 137, 139

Offset: 1

Author

Gus Wiseman, Jul 05 2018

Keywords

• nonn

Comments

Prime factors counted with multiplicity. - Harvey P. Dale, Sep 28 2018

Examples

			60 = 2*2*3*5 has average of prime factors (2+2+3+5)/4 = 3, which is prime, so 60 belongs to the sequence.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Subsequence of A078175.

Cf. A000040, A000607, A056768, A071321, A100118, A316219, A316313.

Programs

Mathematica

Select[Range[100],PrimeQ[Mean[If[#==1,{},Flatten[Cases[FactorInteger[#],{p_,k_}:>Table[p,{k}]]]]]]&]
Select[Range[200],PrimeQ[Mean[Flatten[Table[#[[1]],#[[2]]]&/@ FactorInteger[ #]]]]&] (* Harvey P. Dale, Sep 28 2018 *)

PARI

isok(n) = {my(f=factor(n)); iferr(isprime(sum(k=1, #f~, f[k,1]*f[k,2])/sum(k=1, #f~, f[k,2])), E, 0);} \\ Michel Marcus, Jul 06 2018