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 A181797 a(n) = n multiplied by the sum of its squarefree divisors (A048250(n)). 5
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Sum of reciprocals converges to Pi^2/6. The natural density of positive integers m such that A003557(m) = n equals 6/(a(n)*Pi^2). If m is coprime to 6, a(3m) = a(4m). Apparently the absolute values of the Dirichlet inverse of A000082. - R. J. Mathar, Mar 14 2011 LINKS Amiram Eldar, Table of n, a(n) for n = 1..10000 Wikipedia, Natural density 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 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 MATHEMATICA Table[n*Sum[d*MoebiusMu[d]^2, {d, Divisors[n]}], {n, 1, 50}] (* Vaclav Kotesovec, Feb 02 2019 *) PROG (Sage) A181797 = lambda n: n * sum(d for d in divisors(n) if is_squarefree(d)) # D. S. McNeil, Dec 05 2010 (PARI) a(n)=n*sumdiv(n, d, d*moebius(d)^2) CROSSREFS Cf. A181798, A181799. Sequence in context: A063722 A323058 A072294 * A185152 A028588 A327569 Adjacent sequences:  A181794 A181795 A181796 * A181798 A181799 A181800 KEYWORD nonn,easy,mult AUTHOR Matthew Vandermast, Dec 05 2010 STATUS approved

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Last modified October 16 02:52 EDT 2019. Contains 328038 sequences. (Running on oeis4.)