

A160199


Product of nonexponential divisors of n.


0



1, 1, 1, 1, 1, 6, 1, 4, 1, 10, 1, 24, 1, 14, 15, 8, 1, 54, 1, 40, 21, 22, 1, 2304, 1, 26, 9, 56, 1, 27000, 1, 512, 33, 34, 35, 216, 1, 38, 39, 6400, 1, 74088, 1, 88, 135, 46, 1, 73728, 1, 250, 51, 104, 1, 26244, 55, 12544, 57, 58, 1, 25920000, 1, 62, 189, 512, 65, 287496, 1
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OFFSET

1,6


COMMENTS

The nonexponential divisors of n are those divisors of n that are not exponential divisors of n.


LINKS

Table of n, a(n) for n=1..67.
Eric Weisstein's World of Mathematics, eDivisor


FORMULA

a(n) = A007955(n) / A157488(n).


EXAMPLE

The divisors of 6 are 1, 2, 3, 6. The only exponential divisor of 6 is 6, hence a(6) = 1*2*3 = 6.
The divisors of 16 are 1, 2, 4, 8, 16. The exponential divisors of 16 are 2, 4, 16, hence a(16) = 1*8 = 8.


PROG

(MAGMA) [1] cat [ &*[ d: d in Divisors(n)  exists(t) { p: p in P  v eq 0 or e mod v gt 0 where v is Valuation(d, p) where e is Valuation(n, p) } where P is PrimeDivisors(n) ]: n in [2..67] ]; // Klaus Brockhaus, May 26 2009


CROSSREFS

Cf. A007955 (product of divisors of n), A157488 (product of exponential divisors of n).
Sequence in context: A229606 A101023 A195303 * A178646 A144540 A292107
Adjacent sequences: A160196 A160197 A160198 * A160200 A160201 A160202


KEYWORD

nonn


AUTHOR

Jaroslav Krizek, May 04 2009


EXTENSIONS

Edited by Klaus Brockhaus, May 26 2009


STATUS

approved



