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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
OFFSET
1,1
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 A371812
KEYWORD
nonn
AUTHOR
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