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A162657 Least number m such that n is the denominator of sigma_{-1}(m), or zero if no such exists. 6
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 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois 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: A117885 A030574 A283653 * A145520 A061412 A165646

Adjacent sequences:  A162654 A162655 A162656 * A162658 A162659 A162660

KEYWORD

nonn

AUTHOR

Franklin T. Adams-Watters, Jul 08 2009

STATUS

approved

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Last modified April 26 11:11 EDT 2017. Contains 285444 sequences.