The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A109624

(Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
Showing entries 1-10 | older changes

A109624

Totally multiplicative sequence with a(p) = (p-1)*(p+3) = p^2+2p-3 for prime p.
(history; published version)

#19 by Michael De Vlieger at Sat Nov 05 08:17:52 EDT 2022

STATUS

reviewed

approved

#18 by Joerg Arndt at Sat Nov 05 05:31:48 EDT 2022

STATUS

proposed

reviewed

#17 by Amiram Eldar at Sat Nov 05 04:52:46 EDT 2022

STATUS

editing

proposed

#16 by Amiram Eldar at Sat Nov 05 04:27:14 EDT 2022

FORMULA

Sum_{k=1..n} a(k) ~ c * n^3, where c = 2/(Pi^2 * Product_{p prime} (1 - 3/p^2 + 1/p^3 + 3/p^4) ) = 0.6324191395... . - Amiram Eldar, Nov 05 2022

#15 by Amiram Eldar at Sat Nov 05 04:26:56 EDT 2022

FORMULA

Sum_{k=1..n} a(k) ~ c * n^3, where c = 2/(Pi^2 * Product_{p prime} (1 - (2*3/p-^2 + 1)/p^3) + 3/p^4) = 0.6324191395... . - Amiram Eldar, Nov 05 2022

#14 by Amiram Eldar at Sat Nov 05 04:20:51 EDT 2022

FORMULA

Multiplicative with a(p^e) = ((p-1)*(p+3))^e. If n = Product p(k)^e(k) then a(n) = Product ((p(k)-1)*(p(k)+3))^e(k). a(n) = A003958(n) * A166591(n).

a(n) = A003958(n) * A166591(n).

MATHEMATICA

f[p_, e_] := ((p - 1)*(p + 3))^e; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Nov 05 2022 *)

CROSSREFS

Cf. A003958, A166591.

#13 by Amiram Eldar at Sat Nov 05 04:20:11 EDT 2022

FORMULA

Sum_{k=1..n} a(k) ~ c * n^3, where c = 2/(Pi^2 * Product_{p prime} (1 - (2*p-1)/p^3)) = 0.6324191395... . - Amiram Eldar, Nov 05 2022

STATUS

approved

editing

#12 by Vaclav Kotesovec at Sun Sep 20 05:01:42 EDT 2020

STATUS

editing

approved

#11 by Vaclav Kotesovec at Sun Sep 20 05:01:37 EDT 2020

FORMULA

Sum_{k>=1} 1/a(k) = Product_{primes p} (1 + 1/(p^2 + 2*p - 4)) = 1.471999388763656342016756485604184156984049961181587531678650682804811302... - Vaclav Kotesovec, Sep 20 2020

STATUS

approved

editing

#10 by Vaclav Kotesovec at Sun Sep 20 05:01:03 EDT 2020

STATUS

editing

approved