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A369329
Numbers whose neighbors have a prime number as their greatest odd divisor.
1
4, 6, 11, 12, 13, 18, 21, 23, 25, 27, 30, 39, 42, 45, 47, 57, 60, 72, 75, 81, 87, 93, 95, 102, 105, 108, 117, 123, 135, 138, 147, 150, 159, 165, 177, 180, 192, 193, 198, 207, 213, 225, 228, 240, 270, 273, 282, 297, 303, 312, 315, 327, 333, 345, 348, 357, 383, 385, 387
OFFSET
1,1
COMMENTS
Does this sequence contain a finite or infinite number of squares, powers of 3, even numbers, ...?
MAPLE
filter:= proc(n) local m;
andmap(m -> isprime(m/2^padic:-ordp(m, 2)), [n-1, n+1])
end proc:
select(filter, [$1..1000]); # Robert Israel, Jan 24 2024
MATHEMATICA
q[n_] := PrimeQ[n / 2^IntegerExponent[n, 2]]; Select[Range[400], And @@ q /@ {# - 1, # + 1} &] (* Amiram Eldar, Jan 20 2024 *)
PROG
(Magma) [k: k in [2..400] | #Divisors(2*k-2)-#Divisors(k-1) eq 2 and #Divisors(2*k+2)-#Divisors(k+1) eq 2];
CROSSREFS
Supersequence of A014574 and A276136.
Sequence in context: A322577 A013018 A031271 * A180713 A126591 A031452
KEYWORD
nonn
AUTHOR
STATUS
approved