A385564 Prime powers k such that lcm(1, 2, 3, ..., k)-1 is prime.
3, 4, 5, 7, 8, 19, 23, 29, 32, 47, 61, 97, 181, 233, 307, 401, 887, 1021, 1087, 1361, 1481, 2053, 2293, 5407, 5857, 11059, 14281, 27277, 27803, 36497, 44987, 53017
Offset: 1
Keywords
Examples
k=32 is a prime power, so point at which A003418 attains a new value, namely lcm(1, 2, 3, ..., 32) = 144403552893600, and by subtracting one we get 144403552893599 which is a prime number, so 32 is a member of the sequence.
Crossrefs
Programs
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Mathematica
Select[Range[6000],PrimePowerQ[#]&&PrimeQ[Fold[LCM,Range[#]]-1]&] (* James C. McMahon, Jul 09 2025 *)
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PARI
L=1;for(k=2,6000,!isprimepower(k,&p)&&next();L*=p;ispseudoprime(L-1)&&print1(k,", "))
Extensions
a(31)-a(32) from Michael S. Branicky, Jul 03 2025
Comments