A213401 Smallest number k such that the sum of divisors of k equals n times a square > 1.

3, 7, 6, 22, 19, 14, 12, 21, 22, 27, 43, 33, 198, 28, 24, 66, 67, 30, 98, 57, 44, 197, 367, 42, 343, 63, 85, 91, 463, 54, 48, 93, 86, 202, 76, 66, 511, 111, 99, 120, 163, 60, 1285, 129, 88, 274, 751, 105, 364, 199, 134, 198, 211, 102, 763, 84, 147, 346, 1765

Offset: 1

Author

Michel Lagneau, Jun 10 2012

Keywords

• nonn

Comments

Smallest k such that sigma(k) = n*q^2.

Examples

			a(8) = 21 because the sum of the divisors of 21 is 1 + 3 + 7 +21 = 32 = 8*4 where 4 is a square.
		

Links

• Michel Lagneau, Table of n, a(n) for n = 1..1500

Crossrefs

Cf. A000203, A090688, A213386.

Programs

Maple

a:= proc(n) local k, p;
for k from 1 while irem(sigma(k), n, 'p')>0 or
sqrt(p)<>floor(sqrt(p)) or p=1 do od; k
end:
seq (a(n), n=1..100);

Mathematica

snk[n_]:=Module[{k=2,c},c=Sqrt[DivisorSigma[1,k]/n];While[!IntegerQ[c] || c==1,k++;c=Sqrt[DivisorSigma[1,k]/n]];k]; Array[snk,60] (* Harvey P. Dale, Aug 27 2013 *)