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A146982 Numbers k such that Product{i=1..k}[sigma_0(i)] / k is an integer. 2
1, 2, 4, 6, 8, 9, 12, 16, 18, 20, 24, 27, 30, 32, 36, 40, 45, 48, 50, 54, 60, 64, 70, 72, 75, 80, 81, 84, 90, 96, 100, 105, 108, 112, 120, 125, 126, 128, 135, 140, 144, 150, 160, 162, 168, 175, 180, 189, 192, 196, 200, 210, 216, 224, 225, 240, 243, 245, 250, 252, 256 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

A066843(k)/A000027(k) is an integer.

LINKS

Harvey P. Dale, Table of n, a(n) for n = 1..1000

MATHEMATICA

With[{nn=300}, Select[Thread[{FoldList[Times, DivisorSigma[0, Range[ nn]]], Range[ nn]}], IntegerQ[#[[1]]/#[[2]]]&]][[All, 2]] (* Harvey P. Dale, Mar 05 2019 *)

PROG

(MAGMA) [ n: n in [1..260] | &*[ NumberOfDivisors(k): k in [1..n] ] mod n eq 0 ]; // Klaus Brockhaus, Nov 05 2008

(PARI) isok(k) = frac(prod(i=1, k, numdiv(i))/k) == 0; \\ Michel Marcus, Feb 06 2018

CROSSREFS

Cf. A066843, A000005, A000027.

Sequence in context: A118363 A337674 A324521 * A298305 A090958 A245047

Adjacent sequences:  A146979 A146980 A146981 * A146983 A146984 A146985

KEYWORD

nonn

AUTHOR

Ctibor O. Zizka, Nov 04 2008

EXTENSIONS

Extended beyond a(12) by Klaus Brockhaus, Nov 05 2008

STATUS

approved

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Last modified January 16 02:06 EST 2022. Contains 350374 sequences. (Running on oeis4.)