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.

A167335 Totally multiplicative sequence with a(p) = 2*(3p+1) = 6p+2 for prime p.

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%I A167335 #12 Oct 19 2023 02:16:34
%S A167335 1,14,20,196,32,280,44,2744,400,448,68,3920,80,616,640,38416,104,5600,
%T A167335 116,6272,880,952,140,54880,1024,1120,8000,8624,176,8960,188,537824,
%U A167335 1360,1456,1408,78400,224,1624,1600,87808,248,12320,260,13328,12800
%N A167335 Totally multiplicative sequence with a(p) = 2*(3p+1) = 6p+2 for prime p.
%H A167335 G. C. Greubel, <a href="/A167335/b167335.txt">Table of n, a(n) for n = 1..1000</a>
%F A167335 Multiplicative with a(p^e) = (2*(3p+1))^e. If n = Product p(k)^e(k) then a(n) = Product (2*(3*p(k)+1))^e(k).
%F A167335 a(n) = A061142(n) * A166661(n) = 2^bigomega(n) * A166661(n) = 2^A001222(n) * A166661(n).
%t A167335 a[1] = 1; a[n_] := (fi = FactorInteger[n]; Times @@ ((3*fi[[All, 1]] + 1)^fi[[All, 2]])); Table[a[n]*2^PrimeOmega[n], {n, 1, 100}] (* _G. C. Greubel_, Jun 06 2016 *)
%t A167335 f[p_, e_] := (6*p+2)^e; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* _Amiram Eldar_, Oct 19 2023 *)
%Y A167335 Cf. A001222, A061142, A166661.
%K A167335 nonn,easy,mult
%O A167335 1,2
%A A167335 _Jaroslav Krizek_, Nov 01 2009