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A172333
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Numbers m such that m and m+22 have the same sum of divisors.
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2
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57, 85, 213, 224, 354, 476, 568, 594, 812, 1218, 1235, 1316, 1484, 2103, 2470, 2492, 2643, 2840, 2996, 3836, 3978, 4026, 4544, 4810, 4844, 5012, 6125, 6356, 6524, 7364, 7532, 7648, 8876, 9272, 9328, 10098, 11107, 11797, 12572, 12594, 13412, 13640
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OFFSET
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1,1
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COMMENTS
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If 3*k-1 and 14*k-1 are both prime with k>1, then n = 28*(3*k-1) belongs to this sequence. The number of such integers n <= x would be asymptotically cx/(log x)^2 for some constant c > 0 from the Hardy-Littlewood conjecture D in Partitio Numerorum. - Tomohiro Yamada, Oct 03 2018
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REFERENCES
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J.-M. De Koninck, Ces nombres qui nous fascinent, Entry 62, p. 22, Ellipses, Paris 2008.
W. Sierpinski, A Selection of Problems in the Theory of Numbers. Macmillan, NY, 1964, p. 110.
Tomohiro Yamada, On equations sigma(n) = sigma(n+k) and phi(n) = phi(n+k), J. Comb. Number Theory 9 (2017), 15-21.
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LINKS
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MAPLE
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with(numtheory):for n from 1 to 20000 do; if sigma(n) = sigma(n+22) then print(n); else fi ; od;
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PROG
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(PARI) isok(k) = sigma(k)==sigma(k+22); \\ Altug Alkan, Oct 03 2018
(GAP) Filtered([1..13700], k->Sigma(k)=Sigma(k+22)); # Muniru A Asiru, Oct 20 2018
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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