A166646 Totally multiplicative sequence with a(p) = 6*(p+1) for prime p.

1, 18, 24, 324, 36, 432, 48, 5832, 576, 648, 72, 7776, 84, 864, 864, 104976, 108, 10368, 120, 11664, 1152, 1296, 144, 139968, 1296, 1512, 13824, 15552, 180, 15552, 192, 1889568, 1728, 1944, 1728, 186624, 228, 2160, 2016, 209952, 252, 20736, 264, 23328

Offset

1,2

Links

G. C. Greubel, Table of n, a(n) for n = 1..10000

Formula

Multiplicative with a(p^e) = (6*(p+1))^e. If n = Product p(k)^e(k) then a(n) = Product (6*(p(k)+1)^e(k).

a(n) = A165827(n) * A003959(n) = 6^bigomega(n) * A003959(n) = 6^A001222(n) * A003959(n).

Mathematica

a[1] = 1; a[n_] := (fi = FactorInteger[n]; Times @@ ((fi[[All, 1]] + 1)^fi[[All, 2]])); Table[a[n]*6^(PrimeOmega[n]), {n, 1, 100}] (* G. C. Greubel, May 20 2016 *)
f[p_, e_] := (6*(p+1))^e; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Oct 18 2023 *)

Prog

(PARI) a(n) = {my(f = factor(n)); for (k=1, #f~, f[k, 1] = 6*(f[k, 1]+1)); factorback(f); } \\ Michel Marcus, May 21 2016

Crossrefs

Cf. A001222, A003959, A165827.

Sequence in context: A369540 A125261 A248102 * A109144 A166471 A072422

Adjacent sequences: A166643 A166644 A166645 * A166647 A166648 A166649

Keyword

nonn,easy,mult

Author

Jaroslav Krizek, Oct 18 2009

Status

approved