BBC Russian

Svoboda | Graniru | BBC Russia | Golosameriki | Facebook

The OEIS is supported by the many generous donors to the OEIS Foundation.

Revision History for A091050

(Underlined text is an addition; strikethrough text is a ~~deletion~~.)
Showing entries 1-10 | older changes

A091050

Number of divisors of n that are perfect powers.
(history; published version)

#44 by Joerg Arndt at Sun Dec 31 06:23:31 EST 2023

STATUS

reviewed

approved

#43 by Michel Marcus at Sun Dec 31 03:30:56 EST 2023

STATUS

proposed

reviewed

#42 by Amiram Eldar at Sun Dec 31 01:01:57 EST 2023

STATUS

editing

proposed

#41 by Amiram Eldar at Sun Dec 31 00:50:07 EST 2023

COMMENTS

a(n)=1 iff n is squarefree: a(A005117(n))=1, a(A013929(n))>1;

a(p^k)=k for p prime, k>0: a(A000961(n))=A025474(n);

notNot the same as A005361: a(72)=5 <> A005361(72)=6.

FORMULA

a(n) = 1 iff n is squarefree: a(A005117(n)) = 1, a(A013929(n)) > 1.

a(p^k) = k for p prime, k>0: a(A000961(n)) = A025474(n).

CROSSREFS

Cf. A091051A000005, A001597, A000005A005361, A072102, A091051.

#40 by Amiram Eldar at Sun Dec 31 00:48:30 EST 2023

	FORMULA	`Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 1 + A072102 = 1.874464... . - Amiram Eldar, Dec 31 2023`
	CROSSREFS	`Cf. A091051, A001597, A000005, A072102.`

#39 by Amiram Eldar at Sun Dec 31 00:48:04 EST 2023

LINKS

Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PerfectPower.html">Perfect Power</a>.

#38 by Amiram Eldar at Sun Dec 31 00:47:49 EST 2023

LINKS

Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PerfectPower.html">Perfect Power</a>>.

Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/DivisorFunction.html">Divisor Function</a>>.

STATUS

approved

editing

#37 by Alois P. Heinz at Sun Aug 30 20:19:54 EDT 2020

STATUS

proposed

approved

#36 by Andrew Howroyd at Sun Aug 30 18:30:56 EDT 2020

STATUS

editing

proposed

#35 by Andrew Howroyd at Sun Aug 30 18:21:22 EDT 2020

FORMULA

a(n) = sum (A075802(A027750(n,k)): Sum_{k=1..A000005(n)} A075802(A027750(n,k)). - Reinhard Zumkeller, Dec 13 2012

PROG

(PARI) a(n)={my(f=factor(n)[, 2]); 1 + if(#f, sum(k=2, vecmax(f), moebius(k)*(1 - prod(i=1, #f, 1 + f[i]\k))))} \\ Andrew Howroyd, Aug 30 2020

STATUS

approved

editing

License Agreements, Terms of Use, Privacy Policy. .

Last modified August 22 04:22 EDT 2024. Contains 375356 sequences. (Running on oeis4.)