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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 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 Cf. A007716, A020639, A034691, A255397, A296560, A300335, A317546. Sequence in context: A234541 A066389 A077191 * A319002 A050363 A308063 Adjacent sequences: A317542 A317543 A317544 * A317546 A317547 A317548 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.)