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A167342 Totally multiplicative sequence with a(p) = p*(p+3) = p^2+3p for prime p. 1
1, 10, 18, 100, 40, 180, 70, 1000, 324, 400, 154, 1800, 208, 700, 720, 10000, 340, 3240, 418, 4000, 1260, 1540, 598, 18000, 1600, 2080, 5832, 7000, 928, 7200, 1054, 100000, 2772, 3400, 2800, 32400, 1480, 4180, 3744, 40000, 1804, 12600, 1978, 15400, 12960 (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*(p+3))^e. If n = Product p(k)^e(k) then a(n) = Product (p(k)*(p(k)+3))^e(k). a(n) = n * A166591(n).

Sum_{k>=1} 1/a(k) = Product_{primes p} (1 + 1/(p^2 + 3*p - 1)) = 1.256741057020447773244230946716370792268447699628630376844295183469512964116... - Vaclav Kotesovec, Sep 20 2020

MATHEMATICA

a[1] = 1; a[n_] := (fi = FactorInteger[n]; Times @@ ((fi[[All, 1]] + 3)^fi[[All, 2]])); Table[a[n]*n, {n, 1, 100}] (* G. C. Greubel, Jun 10 2016 *)

CROSSREFS

Sequence in context: A241053 A068642 A198309 * A288781 A233451 A177172

Adjacent sequences:  A167339 A167340 A167341 * A167343 A167344 A167345

KEYWORD

nonn,mult

AUTHOR

Jaroslav Krizek, Nov 01 2009

STATUS

approved

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Last modified April 19 17:46 EDT 2021. Contains 343117 sequences. (Running on oeis4.)