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A050379 Number of ordered factorizations of n into members of A050376. 2
1, 1, 1, 2, 1, 2, 1, 3, 2, 2, 1, 5, 1, 2, 2, 6, 1, 5, 1, 5, 2, 2, 1, 10, 2, 2, 3, 5, 1, 6, 1, 10, 2, 2, 2, 14, 1, 2, 2, 10, 1, 6, 1, 5, 5, 2, 1, 22, 2, 5, 2, 5, 1, 10, 2, 10, 2, 2, 1, 18, 1, 2, 5, 18, 2, 6, 1, 5, 2, 6, 1, 32, 1, 2, 5, 5, 2, 6, 1, 22, 6, 2, 1, 18, 2, 2, 2, 10, 1, 18, 2, 5, 2, 2, 2 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

a(n) depends only on prime signature of n (cf. A025487). So a(24) = a(375) since 24 = 2^3 * 3 and 375 = 3 * 5^3 both have prime signature (3,1).

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..65537

Index entries for sequences computed from exponents in factorization of n

FORMULA

Dirichlet g.f.: 1/(1-B(s)) where B(s) is d.g.f. of characteristic function of A050376.

a(p^k) = A023359(k), for any prime p.

a(A002110(n)) = A000142(n) = n!.

a(n) = A050380(A101296(n)). - R. J. Mathar, May 26 2017

MAPLE

read(transforms) :

L := [1] :

for n from 2 to 100  do

    if isA050376(n) then

        L := [op(L), -1] ;

    else

        L := [op(L), 0] ;

    end if;

end do :

a050379 := DIRICHLETi(L) ; # R. J. Mathar, May 26 2017

PROG

(PARI)

A064547(n) = {my(f = factor(n)[, 2]); sum(k=1, #f, hammingweight(f[k])); } \\ Michel Marcus, Feb 10 2016

isA050376(n) = ((1==omega(n)) && (1==A064547(n))); \\ Checking that omega(n) is 1 is just an optimization here.

A050379(n) = if(1==n, n, sumdiv(n, d, if(d<n, isA050376(n/d)*A050379(d), 0))); \\ Antti Karttunen, Oct 20 2017

CROSSREFS

Cf. A002033, A050376, A050377, A050378, A050380.

Cf. also A000142, A002110, A023359.

Sequence in context: A112970 A112971 A299201 * A153024 A066921 A076649

Adjacent sequences:  A050376 A050377 A050378 * A050380 A050381 A050382

KEYWORD

nonn

AUTHOR

Christian G. Bower, Nov 15 1999

STATUS

approved

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Last modified February 23 15:45 EST 2020. Contains 332167 sequences. (Running on oeis4.)