A166643 - OEIS

%I #14 Oct 17 2023 05:42:53

%S 1,9,12,81,18,108,24,729,144,162,36,972,42,216,216,6561,54,1296,60,

%T 1458,288,324,72,8748,324,378,1728,1944,90,1944,96,59049,432,486,432,

%U 11664,114,540,504,13122,126,2592,132,2916,2592,648,144,78732,576,2916

%N Totally multiplicative sequence with a(p) = 3*(p+1) for prime p.

%H G. C. Greubel, <a href="/A166643/b166643.txt">Table of n, a(n) for n = 1..10000</a>

%F Multiplicative with a(p^e) = (3*(p+1))^e. If n = Product p(k)^e(k) then a(n) = Product (3*(p(k)+1)^e(k).

%F a(n) = A165824(n) * A003959(n) = 3^bigomega(n) * A003959(n) = 3^A001222(n) * A003959(n).

%t a[1] = 1; a[n_] := (fi = FactorInteger[n]; Times @@ ((fi[[All, 1]] + 1)^fi[[All, 2]])); Table[a[n]*3^(PrimeOmega[n]), {n, 1, 100}] (* _G. C. Greubel_, May 20 2016 *)

%t f[p_, e_] := (3*(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] = 3*(f[k,1]+1)); factorback(f);} \\ _Michel Marcus_, May 21 2016

%Y Cf. A001222, A003959, A165824.

%K nonn,easy,mult

%O 1,2

%A _Jaroslav Krizek_, Oct 18 2009