A112779 - OEIS

A112779

Largest exponent in the prime factorization of highly composite numbers (definition 1, A002182).

0, 1, 2, 1, 2, 3, 2, 4, 2, 3, 2, 4, 3, 4, 3, 2, 4, 3, 4, 3, 5, 4, 6, 4, 3, 4, 5, 4, 3, 5, 4, 6, 4, 5, 4, 5, 6, 4, 3, 5, 4, 6, 4, 5, 4, 5, 6, 4, 6, 7, 5, 4, 4, 6, 4, 5, 4, 5, 6, 4, 6, 7, 5, 4, 4, 6, 5, 5, 4, 6, 5, 6, 4, 6, 7, 5, 4, 6, 5, 7, 6, 5, 6, 4, 4, 6, 7, 5, 5, 4, 6, 6, 5, 7, 6, 5, 6, 4, 7, 6, 7, 5, 7, 6, 8

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OFFSET

1,3

COMMENTS

Each highly composite number can be written as the product of primorials (A002110); a(n) is also the number of primorials used in the product.

a(i) is the exponent of 2 in the prime factorization of A002182(i), cf. formula. - David A. Corneth, Aug 16 2015; edited by M. F. Hasler, Jan 03 2020

LINKS

T. D. Noe, Table of n, a(n) for n=1..10000 (using Flammenkamp's data)

A. Flammenkamp, First 1200 highly composite numbers

Eric Weisstein's World of Mathematics, Highly Composite Number

FORMULA

a(n) = A007814(A002182(n)). - David A. Corneth, Aug 16 2015