A167337 Totally multiplicative sequence with a(p) = 2*(5p+1) = 10p+2 for prime p.

1, 22, 32, 484, 52, 704, 72, 10648, 1024, 1144, 112, 15488, 132, 1584, 1664, 234256, 172, 22528, 192, 25168, 2304, 2464, 232, 340736, 2704, 2904, 32768, 34848, 292, 36608, 312, 5153632, 3584, 3784, 3744, 495616, 372, 4224, 4224, 553696, 412, 50688

Offset

1,2

Links

G. C. Greubel, Table of n, a(n) for n = 1..1000

Formula

Multiplicative with a(p^e) = (2*(5p+1))^e. If n = Product p(k)^e(k) then a(n) = Product (2*(5*p(k)+1))^e(k).

a(n) = A061142(n) * A166663(n) = 2^bigomega(n) * A166663(n) = 2^A001222(n) * A166663(n).

Mathematica

a[1] = 1; a[n_] := (fi = FactorInteger[n]; Times @@ ((5*fi[[All, 1]] + 1)^fi[[All, 2]])); Table[a[n]*2^PrimeOmega[n], {n, 1, 100}] (* G. C. Greubel, Jun 06 2016 *)
f[p_, e_] := (10*p+2)^e; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Oct 19 2023 *)

Crossrefs

Cf. A001222, A061142, A166663.

Sequence in context: A142347 A217059 A121019 * A216798 A100372 A084996

Adjacent sequences: A167334 A167335 A167336 * A167338 A167339 A167340

Keyword

nonn,easy,mult

Author

Jaroslav Krizek, Nov 01 2009

Status

approved