|
| |
|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
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
|
|
|
|
STATUS
|
approved
|
| |
|
|
