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

1,7

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

Links

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

Formula

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

Example

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

Prog

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

Crossrefs

Cf. A000010, A002180, A002202, A079695.

Sequence in context: A049107 A046597 A107910 * A085006 A300820 A356936

Adjacent sequences: A280798 A280799 A280800 * A280802 A280803 A280804

Keyword

nonn

Author

Altug Alkan, Jan 08 2017

Status

approved