The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A349258 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A349258

a(n) is the number of prime powers (not including 1) that are infinitary divisors of n.
(history; published version)

#22 by Michel Marcus at Fri Sep 29 04:05:56 EDT 2023

STATUS

reviewed

approved

#21 by Joerg Arndt at Fri Sep 29 03:47:51 EDT 2023

STATUS

proposed

reviewed

#20 by Amiram Eldar at Fri Sep 29 03:08:41 EDT 2023

STATUS

editing

proposed

#19 by Amiram Eldar at Fri Sep 29 03:07:19 EDT 2023

FORMULA

Sum_{k=1..n} a(k) ~ n * (log(log(n)) + B + C), where B is Mertens's constant (A077761) and C = Sum_{p prime} f(1/p) = 0.28135949730844648114..., where f(x) = -1 - (x + 1) + (1-x) * Product_{k>=0} (1 + 2*x^(2^k)). - Amiram Eldar, Sep 29 2023

#18 by Amiram Eldar at Fri Sep 29 02:56:12 EDT 2023

FORMULA

Sum_{k=1..n} a(k) ~ n * (log(log(n)) + B + C), where B is Mertens's constant (A077761) and C = Sum_{p prime} f(1/p) = 0.28135949730844648114..., where f(x) = -1 - x + (1-x) * Product_{k>=0} (1 + 2*x^(2^k)). - Amiram Eldar, Sep 29 2023

CROSSREFS

Cf. A000120, A000961, A001222, A036537, A037445, A050376, A077609, A077761, A246655.

STATUS

approved

editing

#17 by Amiram Eldar at Fri Sep 22 10:19:13 EDT 2023

STATUS

editing

approved

#16 by Amiram Eldar at Fri Sep 22 10:19:11 EDT 2023

COMMENTS

The sums of the first 10^k terms for k = 1, 2, ..., are 3, 48, 505, 5144, 51702, 517594, 5177430, 51778516, 517796372, 5177995095, ... Apparently, this sequence has an asymptotic mean 0.517...

KEYWORD

nonn,easy

EXTENSIONS

Wrong comment removed by Amiram Eldar, Sep 22 2023

STATUS

approved

editing

#15 by Amiram Eldar at Sun May 07 06:13:06 EDT 2023

STATUS

editing

approved

#14 by Amiram Eldar at Sun May 07 06:13:05 EDT 2023

COMMENTS

The sums of the first 10^k terms for k = 1, 2, ..., are 3, 48, 505, 5144, 51702, 517594, 5177430, 51778516, 517796372, 5177995095, ... Apparently, this sequence has an asymptotic mean 0.507517...

STATUS

approved

editing

#13 by Susanna Cuyler at Fri Nov 12 22:32:41 EST 2021

STATUS

proposed

approved