A280801 Least k > 0 such that (2*n)^k is in A002202, or 0 if no such k exists.

1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 4, 1, 3, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 5, 1, 1, 2, 1, 1, 2, 3, 1, 1, 1, 1, 15, 1, 2, 1, 2, 1, 3, 1, 1, 1, 1, 1, 1, 1, 2, 1, 3, 1, 7, 2, 1, 1, 1, 1, 2, 1, 1, 1, 3, 1, 2, 1, 1, 3, 3, 1, 8, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 4, 1, 2, 2, 1, 1, 4, 1, 1, 1, 17, 1, 2, 1, 1, 1, 3, 1, 3, 1, 1, 1, 1, 1, 2, 1, 2, 2, 1, 1, 2, 5, 2, 2, 1, 1, 4, 1, 3

Offset: 1

Author

Altug Alkan, Jan 08 2017

Keywords

• nonn

Comments

Least k such that A280801(k) = n, or 0 if no such k exists are 1, 7, 19, 17, 31, 223, 61, 79, 151, 383, 181, 347, 523, 1109, 43, 607, 101, 733, 1033, 409, 1783, 1123, 199, 1471, 1301, 5113, 1801, 2311, 3617, 1699, 1543, 7489, 2663, 4583, 7829, 2749, 4177, 5179, 2389, 13291, 20389, ...

What is the asymptotic behavior of this sequence?

Conjecture: a(n) > 0 for all values of n. - Altug Alkan, Jan 11 2017

Examples

			a(43) = 15 because (43*2)^k is not in A002202 for 0 < k < 15 and 86^15 = 104106241746467411129608011776 is in A002202.
		

Links

• Giovanni Resta, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000010, A002180, A002202, A079695.

Programs

PARI

a(n) = {my(k = 1); while (!istotient((2*n)^k), k++); k; }

Formula

a(n) = 1 for n in A002180; a(n) <> 1 for n in A079695. - Michel Marcus, Jan 08 2017