A166644 - OEIS

%I #20 Feb 06 2025 08:22:44

%S 1,12,16,144,24,192,32,1728,256,288,48,2304,56,384,384,20736,72,3072,

%T 80,3456,512,576,96,27648,576,672,4096,4608,120,4608,128,248832,768,

%U 864,768,36864,152,960,896,41472,168,6144,176,6912,6144,1152,192,331776

%N Totally multiplicative sequence with a(p) = 4*(p+1) for prime p.

%H G. C. Greubel, <a href="/A166644/b166644.txt">Table of n, a(n) for n = 1..10000</a>

%F Multiplicative with a(p^e) = (4*(p+1))^e. If n = Product p(k)^e(k) then a(n) = Product (4*(p(k)+1))^e(k).

%F a(n) = A165825(n) * A003959(n) = 4^bigomega(n) * A003959(n) = 4^A001222(n) * A003959(n).

%t a[1] = 1; a[n_] := (fi = FactorInteger[n]; Times @@ ((fi[[All, 1]] + 1)^fi[[All, 2]])); Table[a[n]*4^(PrimeOmega[n]), {n, 1, 100}] (* _G. C. Greubel_, May 20 2016 *)

%t f[p_, e_] := (4*(p+1))^e; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* _Amiram Eldar_, Oct 17 2023 *)

%o (PARI) a(n) = {my(f = factor(n)); for (k=1, #f~, f[k,1] = 4*(f[k,1]+1)); factorback(f);} \\ _Michel Marcus_, May 21 2016

%Y Cf. A001222, A003959, A165825.

%K nonn,easy,mult,changed

%O 1,2

%A _Jaroslav Krizek_, Oct 18 2009