cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A167325 Totally multiplicative sequence with a(p) = 6*(p+3) for prime p.

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%I A167325 #12 Oct 21 2023 05:33:41
%S A167325 1,30,36,900,48,1080,60,27000,1296,1440,84,32400,96,1800,1728,810000,
%T A167325 120,38880,132,43200,2160,2520,156,972000,2304,2880,46656,54000,192,
%U A167325 51840,204,24300000,3024,3600,2880,1166400,240,3960,3456,1296000,264,64800,276,75600
%N A167325 Totally multiplicative sequence with a(p) = 6*(p+3) for prime p.
%H A167325 G. C. Greubel, <a href="/A167325/b167325.txt">Table of n, a(n) for n = 1..1000</a>
%F A167325 Multiplicative with a(p^e) = (6*(p+3))^e. If n = Product p(k)^e(k) then a(n) = Product (6*(p(k)+3))^e(k).
%F A167325 a(n) = A165827(n) * A166591(n) = 6^bigomega(n) * A166591(n) = 6^A001222(n) * A166591(n).
%t A167325 a[1] = 1; a[n_] := (fi = FactorInteger[n]; Times @@ ((fi[[All, 1]] + 3)^fi[[All, 2]])); Table[a[n]*6^PrimeOmega[n], {n, 1, 100}] (* _G. C. Greubel_, Jun 09 2016 *)
%t A167325 f[p_, e_] := (6*(p+3))^e; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* _Amiram Eldar_, Oct 21 2023 *)
%Y A167325 Cf. A001222, A165827, A166591.
%K A167325 nonn,easy,mult
%O A167325 1,2
%A A167325 _Jaroslav Krizek_, Nov 01 2009