A286499 Primes which divide a term of A073935.

2, 3, 5, 7, 17, 19, 43, 101, 163, 257, 487, 1459, 14407, 26407, 39367, 62501, 65537, 77659, 1020101, 1336337, 86093443, 242121643, 258280327, 3103616899, 4528177054183, 15258789062501, 411782264189299, 21108889701347407, 953735353027359375062501

Offset: 1

Author

John Machacek, May 27 2017

Keywords

• nonn

Comments

A prime p is in this sequence if and only if p-1 = Product_{i} (p_i)^(a_i) with p_j - 1 = Product_{j

This sequence contains all Fermat primes (A019434).

Examples

			p = 43 is in the sequence because 43-1 = 42 = 2*3*7, 7-1 = 6 = 2*3, 3-1 = 2.
		

Links

• John Machacek, Egyptian Fractions and Prime Power Divisors, arXiv:1706.01008 [math.NT], 2017.

Crossrefs

Cf. A073935.

Programs

Mathematica

upTo[mx_] := Block[{ric}, ric[n_, p_] := If[n < mx, Block[{m = n p}, If[PrimeQ[n + 1], Sow[n+1]; ric[n (n + 1), n+1]]; If[IntegerExponent[n, p] == 1, While[m < mx, ric[m, p]; m *= p]]]]; Sort[Reap[ric[1, 2]][[2, 1]]]]; upTo[10^20] (* Giovanni Resta, May 27 2017 *)

Extensions

a(20)-a(29) from Giovanni Resta, May 27 2017

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