A091293 a(n) is the smallest x for which the following quotient is an integer: (sigma(x) + ... + sigma(x+n-1))/sigma(x+(x+1)+ ... + (x+n-1)), i.e., sum(sigma(j))/sigma(sum(j)) for n terms summed up was integer.

1, 1, 424, 7, 13980, 2, 805675056, 15662957033, 7, 42, 48957

Offset

1,3

Comments

Some other values: a(15)=298, a(19)=97.

a(12) > 8*10^10. - Giovanni Resta, May 07 2017

Links

Table of n, a(n) for n=1..11.

Example

n=6: sigma(2) + sigma(3) + ... + sigma(7) = 3 + 4 + 7 + 6 + 12 + 8 = 40 = sigma(2 + 3 + ... + 7) = sigma(27) = 1 + 3 + 9 + 27 = 40; quotient = 1.

Mathematica

g[x_, k_] := Apply[Plus, Table[DivisorSigma[1, x+j], {j, 0, k-1}]]/ DivisorSigma[1, Apply[Plus, Table[x+j, {j, 0, k-1}]]]; Table[x=1; While[!IntegerQ[g[x, n]], x++]; x, {n, 1, 6}]

Crossrefs

Cf. A000203, A091287-A091293.

Sequence in context: A238174 A251013 A230678 * A114808 A134218 A246733

Adjacent sequences: A091290 A091291 A091292 * A091294 A091295 A091296

Keyword

hard,nonn,more

Author

Labos Elemer, Feb 17 2004

Extensions

a(7)-a(11) from Giovanni Resta, May 07 2017

Status

approved