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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 (list; graph; refs; listen; history; text; internal format)
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 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

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

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Last modified October 23 17:37 EDT 2021. Contains 348215 sequences. (Running on oeis4.)