

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.


4



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

ZhiWei Sun, Table of n, a(n) for n = 1..3190
ZhiWei Sun, A new theorem on the primecounting 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: A196537 A173099 A111928 * A329421 A100985 A176802
Adjacent sequences: A248051 A248052 A248053 * A248055 A248056 A248057


KEYWORD

nonn


AUTHOR

ZhiWei Sun, Sep 30 2014


STATUS

approved



