A162538 The smallest number with an arithmetic mean of divisors equal to n; 0 if nonexistent.

1, 3, 5, 7, 0, 11, 13, 21, 17, 19, 0, 23, 45, 39, 29, 31, 0, 46, 37, 57, 41, 43, 0, 47, 0, 99, 53, 91, 0, 59, 61, 93, 86, 67, 116, 71, 73, 111, 125, 79, 0, 83, 0, 129, 89, 0, 0, 141, 97, 0, 101, 103, 0, 107, 109, 188, 113, 0, 0, 158, 169, 183, 166, 127, 261, 131, 0, 201, 137

Offset

1,2

Comments

a(n) is the smallest k such that sigma(k)/tau(k) = A000203(k)/A000005(k) = n.

Zeros occur if n is in A157847 (i.e., not in A157846).

Links

Table of n, a(n) for n=1..69.

Example

a(7)= 13 because sigma(13)=14 and tau(13)= 2 so 14/2 = 7.
a(8)= 21 because sigma(21)=32 and tau(21)= 4 so 32/4 = 8.

Mathematica

Table[SelectFirst[Range[10^3], n*DivisorSigma[0, #]==DivisorSigma[1, #]&], {n, 70}]/.(Missing["NotFound"]->0) (* Harvey P. Dale, Dec 14 2015 *)

Crossrefs

Cf. A003601.

Sequence in context: A225401 A085090 A084713 * A324990 A084712 A371144

Adjacent sequences: A162535 A162536 A162537 * A162539 A162540 A162541

Keyword

nonn

Author

Claudio Meller, Jul 05 2009

Extensions

Edited by R. J. Mathar, Aug 07 2009

Status

approved