A316436 Sum divided by GCD of the integer partition with Heinz number n > 1.

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, 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, 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

Offset: 2

Author

Gus Wiseman, Jul 03 2018

Keywords

• nonn

Comments

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

Links

• Antti Karttunen, Table of n, a(n) for n = 2..65537
• Index entries for sequences computed from indices in prime factorization
• Index entries for sequences related to Heinz numbers

Crossrefs

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

Programs

Maple

a:= n-> (l-> add(i, i=l)/igcd(l[]))(map(i->
      numtheory[pi](i[1])$i[2], ifactors(n)[2])):
seq(a(n), n=2..100);  # Alois P. Heinz, Jul 03 2018

Mathematica

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

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

Extensions

More terms from Antti Karttunen, Sep 10 2018