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

Author

Juri-Stepan Gerasimov, Jan 20 2024

Keywords

• nonn

Comments

Does this sequence contain a finite or infinite number of squares, powers of 3, even numbers, ...?

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Supersequence of A014574 and A276136.

Cf. A038550, A273401, A275418.

Programs

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];

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 *)
Mean/@SequencePosition[Table[If[PrimeQ[Select[Divisors[n],OddQ][[-1]]],1,0],{n,400}],{1,,1}] (* _Harvey P. Dale, Jul 30 2025 *)