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

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

Example

A002182(8) = 48 = 2^4*3, which has largest exponent 4, so a(8)=4.

Prog

(PARI) apply( A112779(n)=valuation(A002182(n), 2), [1..99]) \\ M. F. Hasler, Jan 03 2020

Crossrefs

Cf. A002110, A002182, A002183, A007814, A108602, A112778, A112780, A112781.

Sequence in context: A108380 A361231 A302098 * A366631 A029201 A071283

Adjacent sequences: A112776 A112777 A112778 * A112780 A112781 A112782

Keyword

nonn

Author

Ray Chandler, Nov 11 2005

Status

approved