A131906 Smallest positive integer k with the same sum of squares of divisors as the n-th integer for which such a k exists.

6, 24, 30, 40, 66, 78, 102, 120, 114, 120, 136, 138, 150, 168, 174, 186, 186, 230, 222, 280, 264, 246, 258, 280, 318, 330, 354, 360, 366, 430, 408, 390, 402, 408, 456, 426, 438, 440, 474, 498, 510, 552, 520, 534, 600, 645, 570, 582, 606, 618, 642, 696, 654, 680

Offset: 1

Author

Peter Pein (petsie(AT)dordos.net), Jul 26 2007

Keywords

• easy
• nonn

Examples

			a(5)=66 because A131905(5)=77 and the sum of the squares of the divisors of 77 is 1+49+121+5929=6100 and the sum of the squares of the divisors of 66 is 1+4+9+36+121+484+1089+4356=6100 and there is no smaller positive integer with this squaresum of its divisors
		

Crossrefs

Cf. A069822, A131902-A131908.

Programs

Mathematica

Clear[tmp]; Last@Transpose[ Function[n, (If[Head[ #1] === tmp, #1 = n; Unevaluated[Sequence[]], {n, #1}] & )[tmp[DivisorSigma[2, n]]]] /@ Range[500]]

PARI

lista(nn) = {for (n=1, nn, my(sn = sigma(n,2)); for (k=1, n-1, if (sigma(k, 2) == sn, print1(k, ", "); break);););} \\ Michel Marcus, Apr 03 2015

Formula

a(n)=min(k>0, k has the same sum of squares of divisors as A131905(n))

Extensions

More terms from Michel Marcus, Apr 03 2015