A319567 Product of y divided by the GCD of y to the power of the length of y, where y is the integer partition with Heinz number n.

1, 1, 1, 1, 1, 2, 1, 1, 1, 3, 1, 2, 1, 4, 6, 1, 1, 4, 1, 3, 2, 5, 1, 2, 1, 6, 1, 4, 1, 6, 1, 1, 10, 7, 12, 4, 1, 8, 3, 3, 1, 8, 1, 5, 12, 9, 1, 2, 1, 9, 14, 6, 1, 8, 15, 4, 4, 10, 1, 6, 1, 11, 2, 1, 2, 10, 1, 7, 18, 12, 1, 4, 1, 12, 18, 8, 20, 12, 1, 3, 1, 13

Offset: 0

Author

Gus Wiseman, Sep 23 2018

Keywords

• nonn

Comments

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

Crossrefs

Cf. A003963, A001222, A056239, A067538, A112798, A143773, A289508, A289509, A316430.

Programs

Mathematica

primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
Table[If[n==1,1,Times@@primeMS[n]/GCD@@primeMS[n]^PrimeOmega[n]],{n,100}]

Formula

a(n) = A003963(n) / A289508(n) ^ A001222(n).