A084307 a(n) is the least number x such that gcd(sigma(x), sigma(x+1)) = n.

1, 13, 17, 6, 199, 5, 242, 27, 391, 57, 1296, 22, 882, 12, 648, 93, 175232, 89, 3872, 236, 195, 1032, 4875263, 14, 5739271, 467, 35377, 83, 1882384, 58, 3024, 308, 29240, 201, 1627208, 118, 79524, 147, 1682, 56, 46854024, 82, 229441, 1204, 2047, 6301, 83386957823

Offset: 1

Author

Labos Elemer, Jun 13 2003

Keywords

• nonn

Comments

a(47) > 10^9 if it exists. - Michel Marcus, Sep 01 2019

Examples

			n=9: GCD[sigma[x+1], sigma[x]]=5 holds for {391,799,800,881,...} of which the first is a(9)=391.
		

Crossrefs

Cf. A000203, A060780, A063444.

Programs

Mathematica

f[x_] := GCD[DivisorSigma[1, x], DivisorSigma[1, x+1]] t=Table[0, {256}]; Do[s=f[n]; If[s<257&&t[[s]]==0, t[[s]]=n], {n, 1, 10000000}]; t

PARI

a(n) = my(x=1, sx=sigma(x), y=2, sy=sigma(2)); while(gcd(sx, sy) != n, x++; y++; sx=sy; sy=sigma(y)); x; \\ Michel Marcus, Aug 28 2019

Extensions

a(41) from Rémy Sigrist, Aug 29 2019

a(42)-a(46) from Michel Marcus, Aug 30 2019

a(47) from Giovanni Resta, Oct 29 2019