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
Antti Karttunen, Table of n, a(n) for n = 1..65537
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
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jul 31 2018
EXTENSIONS
More terms from Antti Karttunen, Sep 10 2018
STATUS
approved