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

1,1

Comments

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

Links

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

Example

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.

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 *)

Prog

(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

Crossrefs

Subsequence of A078175.

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

Sequence in context: A334965 A362621 A133811 * A119314 A317923 A371058

Adjacent sequences: A316522 A316523 A316524 * A316526 A316527 A316528

Keyword

nonn

Author

Gus Wiseman, Jul 05 2018

Status

approved