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A095301
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Numbers n such that there is some k < n with n*sigma(k) = k*sigma(n).
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8
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28, 140, 200, 224, 234, 270, 308, 364, 476, 496, 532, 600, 644, 672, 700, 812, 819, 868, 936, 1036, 1148, 1170, 1204, 1316, 1400, 1484, 1488, 1540, 1638, 1652, 1708, 1800, 1820, 1876, 1988, 2016, 2044, 2200, 2212, 2324, 2380, 2464, 2480, 2492, 2574, 2600
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OFFSET
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1,1
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COMMENTS
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Original name: Numbers n such that A094759(n) < n.
Agrees with A050973 without duplicates.
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
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REFERENCES
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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).
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LINKS
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EXAMPLE
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A094759(28) = 6 < 28, hence 28 is in the sequence.
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PROG
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(PARI) for(n=1, 2600, s=sigma(n); k=1; while(n*sigma(k)!=k*s, k++); if(k<n, print1(n, ", ")));
(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); ); )
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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