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
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jul 05 2018
STATUS
approved