The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A167328 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A167328

Totally multiplicative sequence with a(p) = 9*(p+3) for prime p.
(history; published version)

#11 by Joerg Arndt at Sat Oct 21 05:33:31 EDT 2023

STATUS

reviewed

approved

#10 by Michel Marcus at Sat Oct 21 03:07:49 EDT 2023

STATUS

proposed

reviewed

#9 by Amiram Eldar at Sat Oct 21 02:51:27 EDT 2023

STATUS

editing

proposed

#8 by Amiram Eldar at Sat Oct 21 02:36:50 EDT 2023

DATA

1, 45, 54, 2025, 72, 2430, 90, 91125, 2916, 3240, 126, 109350, 144, 4050, 3888, 4100625, 180, 131220, 198, 145800, 4860, 5670, 234, 4920750, 5184, 6480, 157464, 182250, 288, 174960, 306, 184528125, 6804, 8100, 6480, 5904900, 360, 8910, 7776, 6561000, 396, 218700

FORMULA

Multiplicative with a(p^e) = (9*(p+3))^e. If n = Product p(k)^e(k) then a(n) = Product (9*(p(k)+3))^e(k). a(n) = A165830(n) * A166591(n) = 9^bigomega(n) * A166591(n) = 9^A001222(n) * A166591(n).

a(n) = A165830(n) * A166591(n) = 9^bigomega(n) * A166591(n) = 9^A001222(n) * A166591(n).

MATHEMATICA

f[p_, e_] := (9*(p+3))^e; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Oct 21 2023 *)

CROSSREFS

Cf. A001222, A165830, A166591.

KEYWORD

nonn,easy,mult

STATUS

approved

editing

#7 by Joerg Arndt at Fri Jun 10 01:52:24 EDT 2016

STATUS

proposed

approved

#6 by G. C. Greubel at Thu Jun 09 22:59:20 EDT 2016

STATUS

editing

proposed

#5 by G. C. Greubel at Thu Jun 09 22:59:13 EDT 2016

LINKS

G. C. Greubel, <a href="/A167328/b167328.txt">Table of n, a(n) for n = 1..1000</a>

MATHEMATICA

a[1] = 1; a[n_] := (fi = FactorInteger[n]; Times @@ ((fi[[All, 1]] + 3)^fi[[All, 2]])); Table[a[n]*9^PrimeOmega[n], {n, 1, 100}] (* G. C. Greubel, Jun 09 2016 *)

STATUS

approved

editing

#4 by Russ Cox at Fri Mar 30 19:00:22 EDT 2012

AUTHOR

_Jaroslav Krizek (jaroslav.krizek(AT)atlas.cz), _, Nov 01 2009

Discussion

Fri Mar 30

19:00

OEIS Server: https://oeis.org/edit/global/299

#3 by R. J. Mathar at Sun Feb 06 14:26:56 EST 2011

STATUS

proposed

approved

#2 by R. J. Mathar at Sun Feb 06 14:10:38 EST 2011

KEYWORD

nonn,mult

STATUS

approved

proposed