A307539 Heinz numbers of square integer partitions, where the Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k).

1, 2, 9, 125, 2401, 161051, 4826809, 410338673, 16983563041, 1801152661463, 420707233300201, 25408476896404831, 6582952005840035281, 925103102315013629321, 73885357344138503765449, 12063348350820368238715343, 3876269050118516845397872321

Offset: 0

Author

Gus Wiseman, Apr 13 2019

Keywords

• nonn

Examples

			The square partition (4,4,4,4) has Heinz number prime(4)^4 = 7^4 = 2401.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..303

Crossrefs

After a(0) = 1, same as A062457.

Cf. A002024, A047993, A056239, A096771, A106529, A112798, A115720, A174090, A257990, A263297.

Cf. A088218, A330394.

Programs

Maple

a:= n-> mul(ithprime(i), i=[n$n]):
seq(a(n), n=0..20);  # Alois P. Heinz, Mar 03 2020

Mathematica

Table[If[n==0,1,Prime[n]]^n,{n,0,10}]

Formula

a(n) = A330394(A088218(n)). - Alois P. Heinz, Mar 03 2020