A167349 Totally multiplicative sequence with a(p) = (p+1)^2 = p^2+2p+1 for prime p.

1, 9, 16, 81, 36, 144, 64, 729, 256, 324, 144, 1296, 196, 576, 576, 6561, 324, 2304, 400, 2916, 1024, 1296, 576, 11664, 1296, 1764, 4096, 5184, 900, 5184, 1024, 59049, 2304, 2916, 2304, 20736, 1444, 3600, 3136, 26244, 1764, 9216, 1936, 11664, 9216, 5184

Offset

1,2

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) = A003959(n)^2.

Sum_{k>=1} 1/a(k) = Product_{primes p} (1 + 1/(p*(p+2))) = 1.288853271279060013237007191320577437103236294043770723089390440619086825... - Vaclav Kotesovec, Sep 20 2020

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

Sequence in context: A203719 A198308 A375501 * A267763 A340164 A308248

Adjacent sequences: A167346 A167347 A167348 * A167350 A167351 A167352

Keyword

nonn,mult

Author

Jaroslav Krizek, Nov 01 2009

Status

approved