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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 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

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