A166648 Totally multiplicative sequence with a(p) = 8*(p+1) for prime p.

1, 24, 32, 576, 48, 768, 64, 13824, 1024, 1152, 96, 18432, 112, 1536, 1536, 331776, 144, 24576, 160, 27648, 2048, 2304, 192, 442368, 2304, 2688, 32768, 36864, 240, 36864, 256, 7962624, 3072, 3456, 3072, 589824, 304, 3840, 3584, 663552, 336, 49152

Offset

1,2

Links

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

Formula

Multiplicative with a(p^e) = (8*(p+1))^e. If n = Product p(k)^e(k) then a(n) = Product (8*(p(k)+1)^e(k).

a(n) = A165829(n) * A003959(n) = 8^bigomega(n) * A003959(n) = 8^A001222(n) * A003959(n).

Mathematica

a[1] = 1; a[n_] := (fi = FactorInteger[n]; Times @@ ((fi[[All, 1]] + 1)^fi[[All, 2]])); Table[a[n]*8^(PrimeOmega[n]), {n, 1, 100}] (* G. C. Greubel, May 21 2016 *)
f[p_, e_] := (8*(p+1))^e; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Oct 17 2023 *)

Prog

(PARI) a(n) = {my(f = factor(n)); for (k=1, #f~, f[k, 1] = 8*(f[k, 1]+1)); factorback(f); } \\ Michel Marcus, May 21 2016

Crossrefs

Cf. A001222, A003959, A165829.

Sequence in context: A319928 A025102 A188671 * A231468 A366422 A179188

Adjacent sequences: A166645 A166646 A166647 * A166649 A166650 A166651

Keyword

nonn,easy,mult

Author

Jaroslav Krizek, Oct 18 2009

Status

approved