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.

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

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

Zhi-Wei Sun, Table of n, a(n) for n = 1..10000

Zhi-Wei Sun, A new theorem on the prime-counting 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 A348447 A277606

Adjacent sequences: A248005 A248006 A248007 * A248009 A248010 A248011

Keyword

nonn

Author

Zhi-Wei Sun, Sep 29 2014

Status

approved