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A317545
Number of multimin factorizations of n.
13
1, 1, 1, 2, 1, 2, 1, 4, 2, 2, 1, 5, 1, 2, 2, 8, 1, 4, 1, 5, 2, 2, 1, 12, 2, 2, 4, 5, 1, 5, 1, 16, 2, 2, 2, 11, 1, 2, 2, 12, 1, 5, 1, 5, 5, 2, 1, 28, 2, 4, 2, 5, 1, 8, 2, 12, 2, 2, 1, 15, 1, 2, 5, 32, 2, 5, 1, 5, 2, 5, 1, 29, 1, 2, 4, 5, 2, 5, 1, 28, 8, 2, 1, 15, 2, 2, 2, 12, 1, 12, 2, 5, 2, 2, 2, 64, 1, 4, 5, 11, 1, 5, 1, 12, 5
OFFSET
1,4
COMMENTS
A multimin factorizations of n is an ordered factorization of n into factors greater than 1 such that the sequence of minimal primes dividing each factor is weakly increasing.
LINKS
FORMULA
a(1) = 1; a(n > 1) = Sum_{d|(n/p)} a(d), where p is the smallest prime dividing n.
EXAMPLE
The a(36) = 11 multimin factorizations:
(36),
(2*18), (4*9), (6*6), (12*3), (18*2),
(2*2*9), (2*6*3), (4*3*3), (6*2*3),
(2*2*3*3).
MATHEMATICA
a[n_]:=If[n==1, 1, Sum[a[d], {d, Divisors[n/FactorInteger[n][[1, 1]]]}]];
Array[a, 100]
PROG
(PARI) A317545(n) = if(1==n, 1, my(spf = factor(n)[1, 1]); sumdiv(n/spf, d, A317545(d))); \\ Antti Karttunen, Sep 10 2018
(PARI)
memo317545 = Map(); \\ Memoized version.
A317545(n) = if(1==n, 1, if(mapisdefined(memo317545, n), mapget(memo317545, n), my(spf = factor(n)[1, 1], v = sumdiv(n/spf, d, A317545(d))); mapput(memo317545, n, v); (v))); \\ Antti Karttunen, Sep 10 2018
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jul 31 2018
EXTENSIONS
More terms from Antti Karttunen, Sep 10 2018
STATUS
approved