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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 (list; graph; refs; listen; history; text; internal format)
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
CROSSREFS
Sequence in context: A234541 A066389 A077191 * A319002 A050363 A308063
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jul 31 2018
EXTENSIONS
More terms from Antti Karttunen, Sep 10 2018
STATUS
approved

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Last modified June 17 03:50 EDT 2024. Contains 373432 sequences. (Running on oeis4.)