A073541 Numbers k such that 1/(1/sigma(k) + 1/sigma(k+1)) is an integer.

5, 14, 54, 55, 56, 58, 70, 87, 88, 89, 114, 118, 123, 125, 178, 201, 204, 206, 220, 246, 354, 358, 417, 419, 459, 478, 500, 534, 549, 594, 604, 620, 646, 654, 663, 715, 718, 753, 834, 835, 838, 894, 957, 1006, 1018, 1106, 1194, 1239, 1253, 1318, 1334, 1364

Offset: 1

Author

Benoit Cloitre, Aug 27 2002

Keywords

• easy
• nonn

Examples

			1/sigma(54) + 1/sigma(55) = 1/120 + 1/72 = 1/45 so 54 is in the sequence.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000203.

Programs

Mathematica

Select[Range[1400], IntegerQ[1/(1/DivisorSigma[1, # ]+1/DivisorSigma[1, #+1])]&]

PARI

isok(k) = denominator(1/(1/sigma(k) + 1/sigma(k+1))) == 1; \\ Michel Marcus, May 13 2022

Extensions

Edited by Dean Hickerson, Aug 31 2002