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

Author

Michel Marcus, Jan 27 2020

Keywords

• nonn
• more

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.

Examples

			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, ...
		

Crossrefs

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

Programs

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;