A369329 Numbers whose neighbors have a prime number as their greatest odd divisor.

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, ...?

Links

Table of n, a(n) for n=1..59.

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.

Cf. A038550, A273401, A275418.

Sequence in context: A322577 A013018 A031271 * A180713 A126591 A031452

Adjacent sequences: A369326 A369327 A369328 * A369330 A369331 A369332

Keyword

nonn

Author

Juri-Stepan Gerasimov, Jan 20 2024

Status

approved