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

1,3

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

Formula

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

Mathematica

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

Prog

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

Crossrefs

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

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

Cf. also A331297.

Sequence in context: A274061 A284009 A339695 * A243220 A334593 A293596

Adjacent sequences: A326843 A326844 A326845 * A326847 A326848 A326849

Keyword

nonn

Author

Gus Wiseman, Jul 26 2019

Extensions

More terms from Antti Karttunen, Jan 18 2020

Status

approved