A230311 revision #21
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A230311
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Numbers n such that 1^(k*n) + 2^(k*n) + ... + (k*n)^(k*n) == k (mod k*n) for some k; that is, numbers n such that A031971(k*n) == k (mod k*n) for some k.
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13
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OFFSET
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1,2
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COMMENTS
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Least such k is A231409. No other terms for n < 10^110 (see Grau, Oller-Marcen, Sondow (2015) p. 428). - Jonathan Sondow, Nov 30 2013
Same as quotients Q = m/n of solutions to the congruence 1^m + 2^m + . . . + m^m = n (mod m) with n|m. For Q > 1, a necessary condition is that Q be a primary pseudoperfect number A054377. The condition is not sufficient since the primary pseudoperfect number 52495396602 is not a member. - Jonathan Sondow, Jul 13 2014
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LINKS
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FORMULA
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CROSSREFS
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Cf. A231562 (numbers n such that A031971(8490421583559688410706771261086*n) == n (mod 8490421583559688410706771261086*n)).
Cf. A229312 (numbers n such that A031971(47058*n) == n (mod 47058*n)).
Cf. A229313 (numbers n such that A031971(47058*n) <> n (mod 47058*n)).
Cf. A054377 (primary pseudoperfect numbers).
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KEYWORD
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nonn,more,hard
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AUTHOR
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EXTENSIONS
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STATUS
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editing
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