The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A307960 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A307960

Decimal expansion of the asymptotic density of the coreful perfect numbers (A307958) that are generated from even primitives (A307959).
(history; published version)

#20 by Michel Marcus at Sun Jul 02 03:18:33 EDT 2023

STATUS

reviewed

approved

#19 by Amiram Eldar at Sun Jul 02 03:11:05 EDT 2023

STATUS

proposed

reviewed

#18 by Jon E. Schoenfield at Sat Jul 01 13:48:22 EDT 2023

STATUS

editing

proposed

Discussion

Sun Jul 02

03:11

Amiram Eldar: Yes, I think that this is better. Thanks.

#17 by Jon E. Schoenfield at Sat Jul 01 13:42:52 EDT 2023

NAME

The decimal Decimal expansion of the asymptotic density of the coreful perfect numbers (A307958) that are generated from even primitives (A307959).

COMMENTS

Since the coreful perfect numbers are analogous to e-perfect numbers (A054979), the result of Hagis (see the formula and compare to A318645) can be also applied also here.

LINKS

Peter Hagis, <a href="http://dx.doi.org/10.1155/S0161171288000407">Some results concerning exponential divisors</a>, International Journal of Mathematics and Mathematical Sciences, Vol. 11 , No. 2 (1988), pp. 343-349.

FORMULA

Equals Sum_{ij>=1} beta(c(ij))/c(ij), where beta(nk) = (6/Pi^2)*Product_{p|nk}(p/(p+1)) and c(ij) are is the j-th even terms term of A307959.

STATUS

approved

editing

Discussion

Sat Jul 01

13:48

Jon E. Schoenfield: I thought it would be good to reword the phrase that appears in the published version as “c(i) are the even terms of A307959” because the notation “c(i)” should be used to denote the i-th term of the sequence {c(i)}. Is this rewording okay?

#16 by Joerg Arndt at Sat Jul 04 04:24:26 EDT 2020

STATUS

reviewed

approved

#15 by Michel Marcus at Sat Jul 04 03:54:19 EDT 2020

STATUS

proposed

reviewed

#14 by Amiram Eldar at Sat Jul 04 03:40:07 EDT 2020

STATUS

editing

proposed

#13 by Amiram Eldar at Sat Jul 04 03:35:17 EDT 2020

LINKS

Amiram Eldar, <a href="/A307960/b307960.txt">Table of n, a(n) for n = -2..10000</a>

STATUS

approved

editing

#12 by Amiram Eldar at Thu Jul 02 11:54:16 EDT 2020

STATUS

editing

approved

#11 by Amiram Eldar at Thu Jul 02 11:54:14 EDT 2020

MATHEMATICA

f[p_] := 1/(3 * (2^p-1) * 2^(2*p-1)); v = MersennePrimeExponent/@Range[4525]; RealDigits[(6/Pi^2)*Total[f/@v], 10, 100][[1]]

STATUS

approved

editing