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A112779 Largest exponent in the prime factorization of highly composite numbers (definition 1, A002182). 9
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 (list; graph; refs; listen; history; text; internal format)
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: A147301 A108380 A302098 * A029201 A071283 A172986

Adjacent sequences:  A112776 A112777 A112778 * A112780 A112781 A112782

KEYWORD

nonn

AUTHOR

Ray Chandler, Nov 11 2005

STATUS

approved

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Last modified March 7 04:23 EST 2021. Contains 341868 sequences. (Running on oeis4.)