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A167349 Totally multiplicative sequence with a(p) = (p+1)^2 = p^2+2p+1 for prime p. 1
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 (list; graph; refs; listen; history; text; internal format)
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: A174468 A203719 A198308 * A267763 A340164 A308248

Adjacent sequences:  A167346 A167347 A167348 * A167350 A167351 A167352

KEYWORD

nonn,mult

AUTHOR

Jaroslav Krizek, Nov 01 2009

STATUS

approved

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Last modified February 26 17:22 EST 2021. Contains 341632 sequences. (Running on oeis4.)