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A167363 Totally multiplicative sequence with a(p) = (p+3)^2 = p^2+6p+9 for prime p. 1
1, 25, 36, 625, 64, 900, 100, 15625, 1296, 1600, 196, 22500, 256, 2500, 2304, 390625, 400, 32400, 484, 40000, 3600, 4900, 676, 562500, 4096, 6400, 46656, 62500, 1024, 57600, 1156, 9765625, 7056, 10000, 6400, 810000, 1600, 12100, 9216, 1000000, 1936, 90000 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
LINKS
FORMULA
Multiplicative with a(p^e) = ((p+3)^2)^e. If n = Product p(k)^e(k) then a(n) = Product ((p(k)+3)^2)^e(k). a(n) = A166591(n)^2.
Sum_{k>=1} 1/a(k) = Product_{primes p} (1 + 1/(p^2 + 6*p + 8)) = 1.1245403934230393267573507658470307221064356442604979888687782305037985824... - Vaclav Kotesovec, Sep 20 2020
MATHEMATICA
b[1] = 1; b[n_] := (fi = FactorInteger[n]; Times @@ ((fi[[All, 1]] + 3)^fi[[All, 2]])); Table[b[n]^2, {n, 1, 100}] (* G. C. Greubel, Jun 11 2016 *)
CROSSREFS
Cf. A166591.
Sequence in context: A077676 A030671 A030681 * A035383 A179803 A061863
KEYWORD
nonn,mult
AUTHOR
Jaroslav Krizek, Nov 01 2009
STATUS
approved

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Last modified July 18 21:02 EDT 2024. Contains 374388 sequences. (Running on oeis4.)