A162657 Least number m such that n is the denominator of sigma_{-1}(m), or zero if no such exists.

1, 2, 3, 4, 5, 18, 7, 8, 9, 20, 11, 48, 13, 112, 45, 16, 17, 468, 19, 480, 21, 88, 23, 72, 25, 52, 27, 196, 29, 180, 31, 32, 99, 68, 35, 36, 37, 152, 39, 80, 41, 1344, 43, 176, 810, 368, 47, 192, 49, 50, 459, 104, 53, 162, 55, 448, 57, 116, 59, 9360, 61, 1984, 63, 64, 65

Offset

1,2

Comments

First occurrence of n in A017666.

Conjecture: a(n) is never zero. Checking up to 1000000, the smallest number not found is 210; and a(210) = 26611200.

n|a(n), since sigma_{-1}(n) = sigma(n)/n. a(n) = n for n any prime power (and many others).

Up to 1000, the maximum value is a(330) = 1890345600. - Michel Marcus, Aug 14 2012

Actually, a(n) = n, for n in A014567. - Michel Marcus, Dec 28 2013

Up to 10000, the largest term is a(9570) = 22033432080000. - Giovanni Resta, Mar 22 2014

Links

Michel Marcus and Giovanni Resta, Table of n, a(n) for n = 1..10000 (first 1000 terms from Michel Marcus)

Mathematica

a[n_] := Catch[ For[ lim = Quotient[2*10^9, n]*n; k = 0, k <= lim, k = k + n, If[Denominator[ DivisorSigma[-1, k]] == n, Throw[k]]; If[k >= lim, Throw[0]]]]; a[1]=1; Table[ an = a[n]; Print[{n, an}]; an , {n, 1, 1000}] (* Jean-François Alcover, Aug 14 2012 *)

Prog

(PARI) al(n, lim=100000)=local(r, d); r=vector(n); for(k=1, lim, d=denominator(sigma(k, -1)); if(d<=n&&r[d]==0, r[d]=k)); r
a(n, lim=1000000)=forstep(m=n, lim, n, if(denominator(sigma(m, -1))==n, return(m))); 0

Crossrefs

Cf. A017666, A017665, A000203.

Sequence in context: A030574 A325652 A283653 * A333046 A305794 A317944

Adjacent sequences: A162654 A162655 A162656 * A162658 A162659 A162660

Keyword

nonn

Author

Franklin T. Adams-Watters, Jul 08 2009

Status

approved