A326846 Length times maximum of the integer partition with Heinz number n.

0, 1, 2, 2, 3, 4, 4, 3, 4, 6, 5, 6, 6, 8, 6, 4, 7, 6, 8, 9, 8, 10, 9, 8, 6, 12, 6, 12, 10, 9, 11, 5, 10, 14, 8, 8, 12, 16, 12, 12, 13, 12, 14, 15, 9, 18, 15, 10, 8, 9, 14, 18, 16, 8, 10, 16, 16, 20, 17, 12, 18, 22, 12, 6, 12, 15, 19, 21, 18, 12, 20, 10, 21, 24, 9, 24, 10, 18, 22, 15, 8, 26, 23, 16, 14, 28, 20, 20, 24

Offset: 1

Author

Gus Wiseman, Jul 26 2019

Keywords

• nonn

Comments

The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k), so a(n) is the size of the minimal rectangle containing the Young digram of the integer partition with Heinz number n.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537
• Index entries for sequences related to Heinz numbers
• Index entries for sequences computed from indices in prime factorization

Crossrefs

Cf. A047993, A056239, A061395, A106529, A112798.

Cf. A316413, A326836, A326837, A326844, A326845, A326848, A326849.

Cf. also A331297.

Programs

Mathematica

Table[PrimeOmega[n]*PrimePi[FactorInteger[n][[-1,1]]],{n,100}]

PARI

A326846(n) = if(1==n, 0, bigomega(n)*primepi(vecmax(factor(n)[, 1]))); \\ Antti Karttunen, Jan 18 2020

Formula

a(n) = A001222(n) * A061395(n).

Extensions

More terms from Antti Karttunen, Jan 18 2020