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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, 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
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
KEYWORD
nonn
AUTHOR
Altug Alkan, Jan 08 2017
STATUS
approved