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

Author

Ray Chandler, Nov 11 2005

Keywords

• nonn

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

Examples

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

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

Crossrefs

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

Programs

PARI

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

Formula

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