

A248008


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


9



2, 1, 1, 3, 1, 4, 1, 7, 4, 14, 1, 18, 1, 10, 9, 15, 1, 12, 1, 1, 11, 5, 1, 4, 6, 4, 6, 2, 1, 18, 1, 28, 6, 14, 13, 13, 1, 12, 17, 22, 1, 22, 1, 10, 3, 10, 1, 30, 8, 12, 9, 18, 1, 2, 17, 6, 7, 26, 1, 52, 1, 22, 28, 38, 19, 12, 1, 22, 36, 26
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OFFSET

1,1


COMMENTS

Conjecture: a(n) exists for any n > 0.
a(n) = 1 if and only if n is in A230606. Also, if a(i) = j, a(j) <= i.  Derek Orr, Sep 29 2014
Numbers n such that a(n) > n: 1, 10, 12, 108, 1139, ... The next number, if it exists, is greater than 2*10^4.  Derek Orr, Sep 29 2014


LINKS

ZhiWei Sun, Table of n, a(n) for n = 1..10000
ZhiWei Sun, A new theorem on the primecounting function, arXiv:1409.5685, 2014.


EXAMPLE

a(6) = 4 since 4 + 6 = 10 divides sigma(4*6) = 60.


MATHEMATICA

Do[m=1; Label[aa]; If[Mod[DivisorSigma[1, m*n], m+n]==0, Print[n, " ", m]; Goto[bb]]; m=m+1; Goto[aa]; Label[bb]; Continue, {n, 1, 70}]


PROG

(PARI)
a(n)=m=1; while(sigma(m*n)%(m+n), m++); m
vector(100, n, a(n)) \\ Derek Orr, Sep 29 2014


CROSSREFS

Cf. A000203, A248004, A248006, A248007.
Sequence in context: A089141 A336084 A245717 * A327981 A277606 A228267
Adjacent sequences: A248005 A248006 A248007 * A248009 A248010 A248011


KEYWORD

nonn


AUTHOR

ZhiWei Sun, Sep 29 2014


STATUS

approved



