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%I #27 Jul 21 2015 20:07:31
%S 28,140,200,224,234,270,308,364,476,496,532,600,644,672,700,812,819,
%T 868,936,1036,1148,1170,1204,1316,1400,1484,1488,1540,1638,1652,1708,
%U 1800,1820,1876,1988,2016,2044,2200,2212,2324,2380,2464,2480,2492,2574,2600
%N Numbers n such that there is some k < n with n*sigma(k) = k*sigma(n).
%C Original name: Numbers n such that A094759(n) < n.
%C Agrees with A050973 without duplicates.
%C Also numbers n such that the value sigma(n)/n has already been reached before n. If n belongs to the sequence then A214701(n) = A214701(n-1). - _Michel Marcus_, Aug 19 2012
%D B. Spearman and K. S. Williams, Handbook of Estimates in the Theory of Numbers, Carleton Math. Lecture Note Series No. 14, 1975; see p. 3.2, Eq. (3.9).
%H Michel Marcus and Donovan Johnson, <a href="/A095301/b095301.txt">Table of n, a(n) for n = 1..10000</a> (first 180 terms from Michel Marcus)
%H P. Erdős, <a href="https://www.renyi.hu/~p_erdos/1959-21.pdf">Remarks on number theory II: Some problems on the sigma function</a>, Acta Arith., 5 (1959), 171-177.
%e A094759(28) = 6 < 28, hence 28 is in the sequence.
%o (PARI) for(n=1,2600,s=sigma(n);k=1;while(n*sigma(k)!=k*s,k++);if(k<n,print1(n,", ")));
%o (PARI) allab = []; nb = 0; for (i=1, n, ab = sigma(i)/i; already = 0; if (length(allab) > 0, for (j=1, length(allab), if (ab == allab[j], already = 1; break););); if (already == 1, nb++; print1(i, ","), allab = concat(allab, ab););)
%o /* _Michel Marcus_, Aug 19 2012 */
%Y Cf. A000203, A094759, A050973.
%K nonn
%O 1,1
%A _Klaus Brockhaus_, Jun 01 2004
%E New name from _Charles R Greathouse IV_, Jul 21 2015
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