A322569 a(n)=x is the least integer such that gcd(sigma(x), sigma(x+1)) = 2*n.

13, 6, 5, 27, 57, 22, 12, 93, 89, 236, 1032, 14, 467, 83, 58, 308, 201, 118, 147, 56, 82, 1204, 6301, 69, 596, 1142, 106, 91, 4167, 87, 432, 381, 393, 1407, 348, 70, 5912, 453, 233, 417, 13692, 166, 56493, 1118, 88, 6987, 54048, 154, 1843, 4490, 6833, 2574, 633, 689, 1538

Offset: 1

Author

Michel Marcus, Aug 29 2019

Keywords

• nonn

Comments

Bisection of A084307.

Links

• Michel Marcus, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000203, A060780, A084307.

Programs

Magma

sol:=[]; for n in [1..55] do k:=1; while Gcd(DivisorSigma(1,k),DivisorSigma(1,k+1)) ne 2*n do k:=k+1; end while; Append(~sol,k); end for; sol; // Marius A. Burtea, Aug 29 2019

Mathematica

Module[{nn=60000,g},g=GCD@@@Partition[DivisorSigma[1,Range[nn]],2,1];Table[ Position[ g,2n,1,1],{n,55}]]//Flatten (* Harvey P. Dale, Jan 28 2023 *)

PARI

a(n) = my(x=1); while(gcd(sigma(x), sigma(x+1)) != 2*n, x++); x;