A074391 a(n) is the smallest number such that gcd(a(n), sigma(a(n))) = n.

1, 10, 15, 12, 95, 6, 91, 56, 153, 40, 473, 24, 117, 182, 135, 336, 1139, 90, 703, 380, 861, 946, 3151, 168, 3725, 468, 1431, 28, 5017, 570, 775, 992, 891, 2176, 4865, 792, 2701, 1406, 585, 280, 6683, 546, 11051, 1892, 1305, 6302, 13207, 528, 4753, 5800

Offset: 1

Author

Labos Elemer, Aug 23 2002

Keywords

• nonn

Comments

a(n) is the smallest number k such that A017666(k), the denominator of sigma(k)/k, is equal to k/n. - Jaroslav Krizek, Sep 23 2014

Each term a(n) is divisible by its index n. - Michel Marcus, Jan 13 2015

Examples

			n=6: a(6)=6 because gcd(6, sigma(6))=6 and a(6)=6 is the smallest.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..2000

Crossrefs

Cf. A000203, A017666, A073815, A050399, A009195, A009194.

Programs

Magma

A074391:=func; [A074391(n): n in[1..100]] // Jaroslav Krizek, Sep 23 2014

Maple

f:= proc(n) local k;
  for k from n by n do
    if igcd(k, numtheory:-sigma(k))=n then return k fi
  od
end proc:
map(f, [$1..100]); # Robert Israel, Feb 11 2020

Mathematica

f[x_] := GCD[DivisorSigma[1, x], x] t=Table[0, {100}]; Do[s=f[n]; If[s<101&&t[[s]]==0, t[[s]]=n], {n, 1, 1000000}];

PARI

a(n) = my(k=1); while (gcd(sigma(k), k) != n, k++); k; \\ Michel Marcus, Jan 13 2015

Formula

a(n) = Min{x; gcd(x, sigma(x))} = Min{x; gcd(x, A000203(x))} = n. - corrected by Michel Marcus, Jan 13 2015