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A317545 Number of multimin factorizations of n.

%I A317545 #14 Sep 10 2018 19:17:03
%S A317545 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,
%T A317545 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,
%U A317545 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
%N A317545 Number of multimin factorizations of n.
%C A317545 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.
%H A317545 Antti Karttunen, <a href="/A317545/b317545.txt">Table of n, a(n) for n = 1..65537</a>
%F A317545 a(1) = 1; a(n > 1) = Sum_{d|(n/p)} a(d), where p is the smallest prime dividing n.
%e A317545 The a(36) = 11 multimin factorizations:
%e A317545   (36),
%e A317545   (2*18), (4*9), (6*6), (12*3), (18*2),
%e A317545   (2*2*9), (2*6*3), (4*3*3), (6*2*3),
%e A317545   (2*2*3*3).
%t A317545 a[n_]:=If[n==1,1,Sum[a[d],{d,Divisors[n/FactorInteger[n][[1,1]]]}]];
%t A317545 Array[a,100]
%o A317545 (PARI) A317545(n) = if(1==n,1,my(spf = factor(n)[1,1]); sumdiv(n/spf,d,A317545(d))); \\ _Antti Karttunen_, Sep 10 2018
%o A317545 (PARI)
%o A317545 memo317545 = Map(); \\ Memoized version.
%o A317545 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
%Y A317545 Cf. A007716, A020639, A034691, A255397, A296560, A300335, A317546.
%K A317545 nonn
%O A317545 1,4
%A A317545 _Gus Wiseman_, Jul 31 2018
%E A317545 More terms from _Antti Karttunen_, Sep 10 2018