A331813 a(n) is the least k > 1 such that k*A019278(n) belongs to A019278 too, or a(n) = 0 if no such k exists.

2, 2, 2, 2, 4, 4, 2, 7, 2, 4, 8, 2, 3, 2, 2, 4, 2, 64, 3, 64, 4, 8, 7, 4, 15, 3, 50, 2, 2, 50, 2, 7, 29184, 2, 16, 64, 4, 16, 4, 385, 15, 9, 313600, 2, 4, 2793, 4199, 2, 4, 57600

Offset

1,1

Comments

For the 132 terms (< 5*10^11) of the b-file for A019278, and using an extended list of terms, it can be checked that a(n) is not 0, even if the precise value is not known. For instance, a(51) <= 8097830664651.

Then a(52) to a(82) are: 4, 9, 1197, 8, 256, 4, 65155475, 64, 4096, 16, 195205791, 1387, 7, 37791, 4, 119, 8, 35136, 225, 64, 69127695, 2129920, 256, 4, 19671223, 9, 2, 1379763, 8, 90, 4096. And a(83) <= 7758260899200.

a(51) and a(83) are > 10^9.

Links

Table of n, a(n) for n=1..50.

Example

With A019278 starting as 1, 2, 4, 8, 15, 16, 21, 24, 42, 60, 64, ...
one gets the proper multiples 2, 4, 8, 16, 60, 64, ...
and so the sequence begins: 2, 2, 2, 2, 4, 4, ...

Prog

(PARI) a(n, v019278) = my(m = v019278[n]); my(k=2, y = k*m); while (denominator(sigma(sigma(y))/y) != 1, k++; y += m); k;

Crossrefs

Cf. A019278 (integers m such that sigma(sigma(m))/m is an integer).

Sequence in context: A074912 A274207 A158502 * A215244 A195427 A006643

Adjacent sequences: A331810 A331811 A331812 * A331814 A331815 A331816

Keyword

nonn,more

Author

Michel Marcus, Jan 27 2020

Status

approved