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 A101436 Number of exponents in prime factorization of n which are primes. 8
 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 1, 2, 0, 0, 0, 1, 0 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,36 COMMENTS First occurrence of k: 1,4,36,900,44100 (A061742). - Robert G. Wilson v, Jan 25 2005 LINKS Antti Karttunen, Table of n, a(n) for n = 1..10000 Index entries for sequences computed from exponents in factorization of n. 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 Cf. A010051, A061742, A123391, A125029, A125070, A125072. Sequence in context: A160383 A330023 A328891 * A366247 A056170 A248395 Adjacent sequences: A101433 A101434 A101435 * A101437 A101438 A101439 KEYWORD nonn,easy AUTHOR Leroy Quet, Jan 18 2005 EXTENSIONS More terms from Robert G. Wilson v, Jan 25 2005 STATUS approved

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Last modified November 29 12:41 EST 2023. Contains 367445 sequences. (Running on oeis4.)