

A109874


Largest power n that divides A001142(n).


3



1, 2, 2, 4, 4, 6, 5, 7, 8, 10, 9, 12, 11, 12, 12, 16, 14, 18, 16, 18, 20, 22, 19, 22, 24, 22, 23, 28, 26, 30, 25, 30, 32, 30, 36, 36, 36, 36, 40, 40, 36, 42, 40, 39, 44, 46, 40, 45, 44, 46, 48, 52, 45, 50, 49, 54, 56, 58, 54
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OFFSET

2,2


COMMENTS

a(n) = n1, if n is a prime. If n is composite, a(n) is at least 2, obviously. Conjecture: (1) If n is even and n = 2^r*m, m odd and >1, then a(n)= nr1. (2) If n = 2^r then a(n) = n3. (3) If n is odd and composite then a(n) = n2.


LINKS

Table of n, a(n) for n=2..60.


MAPLE

A001142 := proc(n) local k ; mul(k^(2*k1n), k=1..n) ; end: A109874 := proc(n) local a, k; a := A001142(n) ; k := 0 ; while a mod n = 0 and a > 1 do a := a/n ; k := k+1 ; od; RETURN(k) ; end: seq(A109874(n), n=2..60) ; # R. J. Mathar, Aug 15 2007


CROSSREFS

Cf. A001142, A109873.
Sequence in context: A034974 A048275 A211508 * A069345 A007730 A330271
Adjacent sequences: A109871 A109872 A109873 * A109875 A109876 A109877


KEYWORD

nonn


AUTHOR

Amarnath Murthy, Jul 10 2005


EXTENSIONS

Corrected and extended by R. J. Mathar, Aug 15 2007


STATUS

approved



