A181797 a(n) = n multiplied by the sum of its squarefree divisors (A048250(n)).
1, 6, 12, 12, 30, 72, 56, 24, 36, 180, 132, 144, 182, 336, 360, 48, 306, 216, 380, 360, 672, 792, 552, 288, 150, 1092, 108, 672, 870, 2160, 992, 96, 1584, 1836, 1680, 432, 1406, 2280, 2184, 720, 1722, 4032, 1892, 1584, 1080, 3312, 2256, 576, 392, 900
Offset: 1
Links
- Amiram Eldar, Table of n, a(n) for n = 1..10000
- Wikipedia, Natural density
Programs
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Maple
A181797 := proc(n) local f; f := ifactors(n)[2] ; mul( op(1,d)^op(2,d)*( op(1,d)+1),d=f) ; end proc: # R. J. Mathar, Dec 05 2010
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Mathematica
Table[n*Sum[d*MoebiusMu[d]^2, {d, Divisors[n]}], {n, 1, 50}] (* Vaclav Kotesovec, Feb 02 2019 *) -
PARI
a(n)=n*sumdiv(n,d,d*moebius(d)^2)
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Sage
A181797 = lambda n: n * sum(d for d in divisors(n) if is_squarefree(d)) # D. S. McNeil, Dec 05 2010
Formula
a(n) = n*A048250(n). Multiplicative with a(p^e) = (p+1)*p^e.
Dirichlet g.f. zeta(s-1)*zeta(s-2)/zeta(2*s-4). - R. J. Mathar, Mar 14 2011
G.f.: x*f'(x), where f(x) = Sum_{k>=1} mu(k)^2*k*x^k/(1 - x^k). - Ilya Gutkovskiy, Apr 10 2017
Sum_{k=1..n} a(k) ~ n^3 / 3. - Vaclav Kotesovec, Feb 02 2019
Sum_{k>=1} 1/a(k) = Pi^2/6. - Vaclav Kotesovec, Sep 19 2020
Comments