A316436 - OEIS

%I #13 Sep 15 2018 15:54:57

%S 1,1,2,1,3,1,3,2,4,1,4,1,5,5,4,1,5,1,5,3,6,1,5,2,7,3,6,1,6,1,5,7,8,7,

%T 6,1,9,4,6,1,7,1,7,7,10,1,6,2,7,9,8,1,7,8,7,5,11,1,7,1,12,4,6,3,8,1,9,

%U 11,8,1,7,1,13,8,10,9,9,1,7,4,14,1,8,10,15,6,8,1,8,5,11,13,16,11,7,1,9,9,8,1,10,1,9,9

%N Sum divided by GCD of the integer partition with Heinz number n > 1.

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

%H Antti Karttunen, <a href="/A316436/b316436.txt">Table of n, a(n) for n = 2..65537</a>

%H <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>

%H <a href="/index/He#Heinz">Index entries for sequences related to Heinz numbers</a>

%p a:= n-> (l-> add(i, i=l)/igcd(l[]))(map(i->

%p       numtheory[pi](i[1])$i[2], ifactors(n)[2])):

%p seq(a(n), n=2..100);  # _Alois P. Heinz_, Jul 03 2018

%t Table[With[{pms=If[n===1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]]},Total[pms]/GCD@@pms],{n,2,100}]

%o (PARI) A316436(n) = { my(f = factor(n), pis = apply(p -> primepi(p), f[, 1]~), es = f[, 2]~, g = gcd(pis)); sum(i=1, #f~, pis[i]*es[i])/g; }; \\ _Antti Karttunen_, Sep 10 2018

%Y Cf. A056239, A289508, A289509, A290103, A290104, A296150, A316430, A316431, A316432, A316437.

%K nonn

%O 2,3

%A _Gus Wiseman_, Jul 03 2018

%E More terms from _Antti Karttunen_, Sep 10 2018