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Number of multimin factorizations of n.
13

%I #14 Sep 10 2018 19:17:03

%S 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 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 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 Number of multimin factorizations of n.

%C 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 Antti Karttunen, <a href="/A317545/b317545.txt">Table of n, a(n) for n = 1..65537</a>

%F a(1) = 1; a(n > 1) = Sum_{d|(n/p)} a(d), where p is the smallest prime dividing n.

%e The a(36) = 11 multimin factorizations:

%e (36),

%e (2*18), (4*9), (6*6), (12*3), (18*2),

%e (2*2*9), (2*6*3), (4*3*3), (6*2*3),

%e (2*2*3*3).

%t a[n_]:=If[n==1,1,Sum[a[d],{d,Divisors[n/FactorInteger[n][[1,1]]]}]];

%t Array[a,100]

%o (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 (PARI)

%o memo317545 = Map(); \\ Memoized version.

%o 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 Cf. A007716, A020639, A034691, A255397, A296560, A300335, A317546.

%K nonn

%O 1,4

%A _Gus Wiseman_, Jul 31 2018

%E More terms from _Antti Karttunen_, Sep 10 2018