A248054 - OEIS

A248054

Least positive integer m such that m + n divides sigma(m^2) + sigma(n^2), where sigma(k) is the sum of all positive divisors of k.

1, 3, 2, 7, 24, 34, 3, 81, 209, 16, 63, 25, 7, 20, 140, 10, 3, 10, 22, 2, 39, 4, 35, 5, 4, 2, 28, 27, 75, 41, 16, 78, 44, 6, 23, 14, 207, 59, 21, 84, 17, 78, 7, 3, 11725, 10, 5, 2, 1669, 361, 134, 10, 141, 310, 21, 73, 21, 33, 38, 121

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OFFSET

1,2

COMMENTS

Conjecture: a(n) exists for any n > 0.

LINKS

Zhi-Wei Sun, Table of n, a(n) for n = 1..3190

Zhi-Wei Sun, A new theorem on the prime-counting function, arXiv:1409.5685, 2014.

EXAMPLE

a(4) = 7 since 7 + 4 = 11 divides sigma(7^2) + sigma(4^2) = 57 + 31 = 88.

MATHEMATICA

Do[m=1; Label[aa]; If[Mod[DivisorSigma[1, m^2]+DivisorSigma[1, n^2], m+n]==0, Print[n, " ", m]; Goto[bb]]; m=m+1; Goto[aa]; Label[bb]; Continue, {n, 1, 60}]

CROSSREFS

Cf. A000203, A248008, A248036, A248052.

Sequence in context: A173099 A111928 A348695 * A375612 A329421 A100985

Adjacent sequences: A248051 A248052 A248053 * A248055 A248056 A248057

KEYWORD

nonn

AUTHOR

Zhi-Wei Sun, Sep 30 2014

STATUS

approved