A331019 a(n) is the least k such that the denominator(sigma(sigma(k*n))/(k*n)) equals n.

1, 15, 1, 8, 1, 144, 1, 16, 1, 1, 1, 8, 1, 255, 3, 16, 1, 12, 1, 2, 7, 1, 1, 288, 1, 18, 21, 8, 1, 84, 1, 13, 1, 11, 1, 4096, 1, 4, 3, 270, 1, 2448, 1, 2, 3, 1, 1, 16, 1, 420, 3, 1, 1, 124, 3, 16, 3, 128, 1, 616, 1, 85, 3, 16, 1, 1, 1, 8, 3, 1, 1, 32, 1, 64

Offset: 1

Author

Ray Chandler, Jan 09 2020

Keywords

• nonn

Comments

a(n) is the least k such that the A318060(k*n) equals n.

Links

• Ray Chandler, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000203 (sigma), A051027 (sigma(sigma)), A318060.

Cf. A019278, A330598, A331033.

Programs

PARI

a(n) = my(k=n); while (denominator(sigma(sigma(k))/k) != n, k+=n); k/n;

Formula

a(n) = A331033(n)/n.