id:A057521 - OEIS Search Results

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Powerful (1) part of n: if n = Product_i (pi^ei) then a(n) = Product_{i : ei > 1} (pi^ei); if n=b*c^2*d^3 then a(n)=c^2*d^3 when b is minimized.

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1, 1, 1, 4, 1, 1, 1, 8, 9, 1, 1, 4, 1, 1, 1, 16, 1, 9, 1, 4, 1, 1, 1, 8, 25, 1, 27, 4, 1, 1, 1, 32, 1, 1, 1, 36, 1, 1, 1, 8, 1, 1, 1, 4, 9, 1, 1, 16, 49, 25, 1, 4, 1, 27, 1, 8, 1, 1, 1, 4, 1, 1, 9, 64, 1, 1, 1, 4, 1, 1, 1, 72, 1, 1, 25, 4, 1, 1, 1, 16, 81, 1, 1, 4, 1, 1, 1, 8, 1, 9, 1, 4, 1, 1, 1, 32, 1 (list; graph; listen)

	OFFSET	`1,4`
	LINKS	`T. D. Noe, Table of n, a(n) for n=1..1000` `Index entries for sequences related to powerful numbers`
	FORMULA	`a(n)=n/A055231(n)` `Multiplicative with a(p)=1 and a(p^e)=p^e for e>1. - Vladeta Jovovic (vladeta(AT)eunet.rs), Nov 01 2001`
	EXAMPLE	`a(40)=8 since 40=2^3*5 so the powerful part is 2^3=8`
	CROSSREFS	`Cf. A001694.` `Sequence in context: A073937 A074058 A088440 this_sequence A084885 A112538 A008477` `Adjacent sequences: A057518 A057519 A057520 this_sequence A057522 A057523 A057524`
	KEYWORD	`nonn,mult`
	AUTHOR	`Henry Bottomley (se16(AT)btinternet.com), Sep 01 2000`

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Last modified December 20 16:54 EST 2009. Contains 171081 sequences.

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