A358527 Position of p in the factorization (without multiplicity) of 2^(p-1)-1, where p is the n-th odd prime.
1, 2, 2, 2, 4, 3, 3, 2, 3, 4, 6, 6, 3, 2, 3, 2, 8, 4, 5, 8, 3, 2, 5, 6, 6, 3, 2, 8, 6, 6, 4, 4, 4, 3, 5, 7, 5, 2, 3, 2, 14, 4, 7, 7, 8, 9, 3, 2, 5, 5, 4, 12, 4, 4, 2, 3, 8, 7, 12, 3, 3, 6, 4, 10, 3, 9, 13, 2, 7, 7, 2, 3, 5, 8, 2, 3, 13, 10, 10, 4, 19, 4, 13, 3
Offset: 1
Keywords
Examples
a(19) = 5 because the 19th odd prime is 71 and 71 is the 5th largest distinct prime factor of 2^(71-1)-1 = 1180591620717411303423 = 3 * 11 * 31 * 43 * 71 * 127 * 281 * 86171 * 122921.
Links
- Amiram Eldar, Table of n, a(n) for n = 1..196
Programs
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Mathematica
Array[FirstPosition[FactorInteger[2^(# - 1) - 1], #][[1]] &[Prime[# + 1]] &, 50] (* Michael De Vlieger, Nov 27 2022 *)
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PARI
a(n) = my(p=prime(n+1), v=factor(2^(p-1)-1)[,1]); vecsearch(v, p); \\ Michel Marcus, Nov 28 2022
Extensions
More terms from Amiram Eldar, Nov 23 2022