

A340815


Prime powers whose neighbors' greatest odd divisors are powers of primes.


0



2, 3, 4, 5, 7, 8, 9, 11, 13, 17, 19, 23, 25, 27, 37, 47, 49, 53, 73, 81, 97, 107, 163, 193, 243, 383, 487, 577, 863, 1153, 2187, 2593, 2917, 4373, 8747, 995327, 1492993, 1594323, 1990657, 5308417, 28311553, 86093443, 6879707137, 1761205026817, 2348273369087
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OFFSET

1,1


LINKS

Table of n, a(n) for n=1..45.


EXAMPLE

2 (greatest odd divisor of neighbor 1 is equal to 1 and greatest odd divisor of neighbor 3 is equal to 3);
3 (2 > 1 and 4 > 1),
4 (3 > 3 and 5 > 5),
5 (4 > 1 and 6 > 3),
7 (6 > 3 and 8 > 1),
8 (7 > 7 and 9 > 9),
9 (8 > 1 and 10 > 5), ...


MATHEMATICA

Select[Select[Range[0, 10000], PrimePowerQ], And@@(If[#==1, True, PrimePowerQ@#]&/@(Max@Select[Divisors@#, OddQ]&/@{#1, #+1}))&] (* Giorgos Kalogeropoulos, Mar 31 2021 *)


PROG

(PARI) isp(m) = my(t=m>>valuation(m, 2)); isprimepower(t)  t==1;
is(k) = isprimepower(k) && isp(k1) && isp(k+1); \\ Jinyuan Wang, Mar 27 2021


CROSSREFS

Cf. A000265 (the greatest odd divisors of n), A000961 (prime powers).
Sequence in context: A277187 A339841 A087797 * A280619 A282136 A153730
Adjacent sequences: A340812 A340813 A340814 * A340816 A340817 A340818


KEYWORD

nonn


AUTHOR

JuriStepan Gerasimov, Mar 24 2021


EXTENSIONS

Name corrected by Jon E. Schoenfield, Mar 24 2021
a(33)a(42) from Jinyuan Wang, Mar 27 2021
a(43)a(45) from Martin Ehrenstein, Apr 28 2021


STATUS

approved



