OFFSET
1,36
COMMENTS
First occurrence of k: 1,4,36,900,44100 (A061742). - Robert G. Wilson v, Jan 25 2005
LINKS
FORMULA
Additive with a(p^e) = A010051(e). - Antti Karttunen, Jul 19 2017
Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = Sum_{p prime} (P(p)-P(p+1)) = 0.39847584805803104040..., where P(s) is the prime zeta function. - Amiram Eldar, Sep 29 2023
EXAMPLE
36 = 2^2 *3^2. Since 2 is a prime and occurs twice as an exponent in the prime factorization of 36, a(36) = 2.
MATHEMATICA
f[n_] := Length[ Select[ Flatten[ Table[ #[[2]], {1}] & /@ FactorInteger[n]], PrimeQ[ # ] &]]; Table[ f[n], {n, 105}] (* Robert G. Wilson v, Jan 25 2005 *)
Table[Count[Transpose[FactorInteger[n]][[2]], _?PrimeQ], {n, 120}] (* Harvey P. Dale, Mar 21 2016 *)
PROG
(PARI) A101436(n) = vecsum(apply(e -> isprime(e), factorint(n)[, 2])); \\ Antti Karttunen, Jul 19 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Leroy Quet, Jan 18 2005
EXTENSIONS
More terms from Robert G. Wilson v, Jan 25 2005
STATUS
approved