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A181797 a(n) = n multiplied by the sum of its squarefree divisors (A048250(n)). 4
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

Table of n, a(n) for n=1..50.

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

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

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: A063648 A063722 A072294 * A185152 A028588 A221433

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 February 25 00:39 EST 2018. Contains 299630 sequences. (Running on oeis4.)