A316555 - OEIS

%I #16 Oct 04 2018 20:05:14

%S 0,1,1,1,1,2,1,1,1,2,1,2,1,2,3,1,1,2,1,2,2,2,1,2,1,2,1,2,1,3,1,1,3,2,

%T 3,2,1,2,2,2,1,3,1,2,3,2,1,2,1,2,3,2,1,2,3,2,2,2,1,3,1,2,2,1,2,3,1,2,

%U 3,3,1,2,1,2,3,2,3,3,1,2,1,2,1,3,3,2,2,2,1,3,3,2,3,2,3,2,1,2,3,2,1,3,1,2,4

%N Number of distinct GCDs of nonempty submultisets of the integer partition with Heinz number n.

%C The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k).

%C Number of distinct values obtained when A289508 is applied to all divisors of n larger than one. - _Antti Karttunen_, Sep 28 2018

%H Antti Karttunen, <a href="/A316555/b316555.txt">Table of n, a(n) for n = 1..65537</a>

%e 455 is the Heinz number of (6,4,3) which has possible GCDs of nonempty submultisets {1,2,3,4,6} so a(455) = 5.

%t Table[Length[Union[GCD@@@Rest[Subsets[If[n==1,{},Cases[FactorInteger[n],{p_,k_}:>PrimePi[p]]]]]]],{n,100}]

%o (PARI)

%o A289508(n) = gcd(apply(p->primepi(p),factor(n)[,1]));

%o A316555(n) = { my(m=Map(),s,k=0); fordiv(n,d,if((d>1)&&!mapisdefined(m,s=A289508(d)), mapput(m,s,s); k++)); (k); }; \\ _Antti Karttunen_, Sep 28 2018

%Y Cf. A056239, A108917, A122768, A275972, A289508, A289509, A296150, A316313, A316314, A316430, A316556, A316557.

%Y Cf. also A304793, A305611, A319685, A319695 for other similarly constructed sequences.

%K nonn

%O 1,6

%A _Gus Wiseman_, Jul 06 2018

%E More terms from _Antti Karttunen_, Sep 28 2018