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A316525
Numbers whose average of prime factors is prime.
1
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
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
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jul 05 2018
STATUS
approved