The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A073184 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A073184

Number of cubefree divisors of n.
(history; published version)

#36 by Amiram Eldar at Sun Nov 13 05:30:13 EST 2022

STATUS

editing

approved

#35 by Amiram Eldar at Sun Nov 13 05:30:11 EST 2022

FORMULA

a(n) = Sum_{k = 1..A000005(n)} A212793(A027750(n,k)). - _Reinhard Zumkeller, _, May 27 2012

STATUS

approved

editing

#34 by Joerg Arndt at Sat Oct 08 09:44:57 EDT 2022

STATUS

proposed

approved

#33 by Amiram Eldar at Sat Oct 08 03:35:21 EDT 2022

STATUS

editing

proposed

#32 by Amiram Eldar at Sat Oct 08 03:11:46 EDT 2022

EXAMPLE

The divisors of 56 are {1, 2, 4, 7, 8, 14, 28, 56}, 8=2^3 and 56=7*2^3 are not cubefree, therefore a(56) = 6.

CROSSREFS

Cf. A000005, A000012, A001620, A004709, A027750, A034444, A073180, A073183, A073185, A212793.

#31 by Amiram Eldar at Sat Oct 08 03:11:08 EDT 2022

CROSSREFS

Cf. A000005, A073185, A001620, A004709, A073183, A073180, A027750, A034444, A073180, A073183, A073185, A212793.

#30 by Amiram Eldar at Sat Oct 08 03:10:03 EDT 2022

COMMENTS

a(n) <= A073182(n).

FORMULA

a(n) <= A073182(n).

#29 by Amiram Eldar at Sat Oct 08 03:09:30 EDT 2022

COMMENTS

a(n) = sum number of divisors of the cubefree kernel of n: a(n) = A073184A000005(A007948(n)); [corrected by _Amiram Eldar_, Oct 08 2022]

FORMULA

a(n) = sumSum_{k = 1..A000005(n)} A212793(A027750(n,k)): k = 1..A000005(n)). - _Reinhard Zumkeller_, , May 27 2012

Sum_{k=1..n} a(k) ~ n / Zetazeta(3) * (log(n) - 1 + 2*gamma - 3*Zetazeta'(3)/Zetazeta(3)), where gamma is the Euler-Mascheroni constant A001620. - Vaclav Kotesovec, Jan 31 2019

#28 by Amiram Eldar at Sat Oct 08 03:08:17 EDT 2022

PROG

(PARI) a(n) = {my(e = factor(n)[, 2]); prod(i = 1, #e, if(e[i] == 1, 2, 3))}; \\ Amiram Eldar, Oct 08 2022

STATUS

approved

editing

#27 by Vaclav Kotesovec at Thu Jan 31 06:52:39 EST 2019

STATUS

editing

approved