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A125030 a(n) = sum of exponents in the prime factorization of n that are noncomposite. 4
0, 1, 1, 2, 1, 2, 1, 3, 2, 2, 1, 3, 1, 2, 2, 0, 1, 3, 1, 3, 2, 2, 1, 4, 2, 2, 3, 3, 1, 3, 1, 5, 2, 2, 2, 4, 1, 2, 2, 4, 1, 3, 1, 3, 3, 2, 1, 1, 2, 3, 2, 3, 1, 4, 2, 4, 2, 2, 1, 4, 1, 2, 3, 0, 2, 3, 1, 3, 2, 3, 1, 5, 1, 2, 3, 3, 2, 3, 1, 1, 0, 2, 1, 4, 2, 2, 2, 4, 1, 4, 2, 3, 2, 2, 2, 6, 1, 3, 3, 4, 1, 3, 1, 4, 3 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..10000

Index entries for sequences computed from exponents in factorization of n

EXAMPLE

a(720) = 3, since the prime factorization of 720 is 2^4 * 3^2 * 5^1 and two of the exponents in this factorization are noncomposites (the exponents 2 and 1, whose sum is 3).

MATHEMATICA

f[n_] := Plus @@ Select[Last /@ FactorInteger[n], # == 1 || PrimeQ[ # ] &]; Table[f[n], {n, 110}] (* Ray Chandler, Nov 19 2006 *)

PROG

(PARI) A125030(n) = vecsum(apply(e -> if((1==e)||isprime(e), e, 0), factorint(n)[, 2])); \\ Antti Karttunen, Jul 07 2017

CROSSREFS

Cf. A001222, A125029, A125071.

Sequence in context: A325568 A326195 A073811 * A116479 A318322 A122810

Adjacent sequences:  A125027 A125028 A125029 * A125031 A125032 A125033

KEYWORD

nonn

AUTHOR

Leroy Quet, Nov 16 2006

EXTENSIONS

Extended by Ray Chandler, Nov 19 2006

STATUS

approved

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Last modified March 30 22:55 EDT 2020. Contains 333132 sequences. (Running on oeis4.)