A369615 Powers of primes (A000961) whose neighbors have a prime number as their greatest odd divisor.
4, 11, 13, 23, 25, 27, 47, 81, 193, 383, 2187, 1594323
Offset: 1
Examples
(prime = greatest odd divisor of a(n)-1; a(n); prime = greatest odd divisor of a(n)+1): (3; 4; 5), (5; 11; 3), (3; 13; 7), (11; 23; 3), (3; 25; 13), (13; 27; 7), (23; 47; 3), (5; 81; 41), (3; 193; 97), (191; 383; 3), (1093; 2187; 547), (797161; 1594323; 398581).
Programs
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Magma
[k: k in [2..1600000] | #Divisors(2*k-2)-#Divisors(k-1) eq 2 and #PrimeDivisors(k) eq 1 and #Divisors(2*k+2)-#Divisors(k+1) eq 2];
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Mathematica
q[n_] := PrimeQ[n/2^IntegerExponent[n, 2]]; Select[Range[2*10^6], PrimePowerQ[#] && And @@ q /@ {# - 1, # + 1} &] (* Amiram Eldar, Jan 28 2024 *)
Comments