A340815 Prime powers whose neighbors' greatest odd divisors are powers of primes.

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

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(k-1) && isp(k+1); \\ Jinyuan Wang, Mar 27 2021

Crossrefs

Cf. A000265 (the greatest odd divisor 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

Juri-Stepan 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