A105069 Number of distinct prime divisors of 100^n - 3.
1, 2, 2, 2, 2, 2, 2, 4, 4, 4, 2, 2, 3, 3, 3, 4, 2, 4, 3, 5, 5, 4, 4, 5, 4, 4, 2, 4, 5, 4, 3, 4, 3, 5, 5, 3, 5, 5, 4, 4, 5, 5, 2, 3, 6, 4, 4, 8, 4, 4, 6, 3, 4, 6, 6, 5, 6, 5, 5, 3, 3, 7, 8, 5, 5, 3, 3, 5, 4, 1, 6, 4, 5, 6, 3, 5, 6, 6, 4, 5, 7, 3, 3, 7, 3, 6, 4, 5, 6, 8, 2, 7, 3, 4, 8, 6, 6, 7, 5, 4, 8, 6, 6, 5, 4, 4, 6, 4, 3, 5, 7
Offset: 1
Keywords
Examples
If n = 1, then 100^1 - 3 = 97 which is prime so the first term is 1.
Programs
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Maple
A105069 := proc(n) 100^n-3 ; numtheory[factorset](%) ; nops(%) ; end proc: # R. J. Mathar, Aug 24 2011
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Mathematica
Table[PrimeNu[(100)^n - 3], {n, 1, 50}] (* G. C. Greubel, May 07 2017 *)
Formula
a(n) = A001221(100^n-3).
a(n) = A105068(2*n). - Amiram Eldar, Jan 25 2020
Extensions
a(31)-a(60) from Amiram Eldar, Jan 25 2020
a(61)-a(66) from Jinyuan Wang, Apr 01 2020
a(67)-a(111) from Michael S. Branicky, Apr 14 2023 using factorbd.com