A167302 Totally multiplicative sequence with a(p) = 10*(p-2) for prime p.

1, 0, 10, 0, 30, 0, 50, 0, 100, 0, 90, 0, 110, 0, 300, 0, 150, 0, 170, 0, 500, 0, 210, 0, 900, 0, 1000, 0, 270, 0, 290, 0, 900, 0, 1500, 0, 350, 0, 1100, 0, 390, 0, 410, 0, 3000, 0, 450, 0, 2500, 0, 1500, 0, 510, 0, 2700, 0, 1700, 0, 570, 0, 590, 0, 5000, 0, 3300

Offset

1,3

Links

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

Formula

Multiplicative with a(p^e) = (10*(p-2))^e. If n = Product p(k)^e(k) then a(n) = Product (10*(p(k)-2))^e(k).

a(2k) = 0 for k >= 1.

a(n) = A165831(n) * A166586(n) = 10^bigomega(n) * A166586(n) = 10^A001222(n) * A166586(n).

Mathematica

a[1] = 1; a[n_] := (fi = FactorInteger[n]; Times @@ ((fi[[All, 1]] - 2)^fi[[All, 2]])); Table[a[n]*10^PrimeOmega[n], {n, 1, 100}] (* G. C. Greubel, Jun 07 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, A165831, A166586.

Sequence in context: A087474 A051906 A171809 * A302576 A214122 A084033

Adjacent sequences: A167299 A167300 A167301 * A167303 A167304 A167305

Keyword

nonn,easy,mult

Author

Jaroslav Krizek, Nov 01 2009

Status

approved