A167343 Totally multiplicative sequence with a(p) = (p-1)^2 = p^2-2p+1 for prime p.

1, 1, 4, 1, 16, 4, 36, 1, 16, 16, 100, 4, 144, 36, 64, 1, 256, 16, 324, 16, 144, 100, 484, 4, 256, 144, 64, 36, 784, 64, 900, 1, 400, 256, 576, 16, 1296, 324, 576, 16, 1600, 144, 1764, 100, 256, 484, 2116, 4, 1296, 256

Offset

1,3

Links

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

Formula

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

a(n) = A003958(n)^2.

Sum_{k=1..n} a(k) ~ c * n^3, where c = (2/Pi^2) / Product_{p prime} (1 + 1/p^2 + 1/p^3 - 1/p^4) = 0.1229567616... . - Amiram Eldar, Dec 15 2022

Mathematica

a[1] = 1; a[n_] := (fi = FactorInteger[n]; Times @@ ((fi[[All, 1]] - 1)^fi[[All, 2]])); Table[a[n]^2, {n, 1, 100}] (* G. C. Greubel, Jun 10 2016 *)

Crossrefs

Cf. A003958.

Sequence in context: A309074 A175844 A351434 * A094361 A187926 A285281

Adjacent sequences: A167340 A167341 A167342 * A167344 A167345 A167346

Keyword

nonn,mult

Author

Jaroslav Krizek, Nov 01 2009

Status

approved