A238161 Greatest common divisor of the prime factors of n, each increased by 1.
3, 4, 3, 6, 1, 8, 3, 4, 3, 12, 1, 14, 1, 2, 3, 18, 1, 20, 3, 4, 3, 24, 1, 6, 1, 4, 1, 30, 1, 32, 3, 4, 3, 2, 1, 38, 1, 2, 3, 42, 1, 44, 3, 2, 3, 48, 1, 8, 3, 2, 1, 54, 1, 6, 1, 4, 3, 60, 1, 62, 1, 4, 3, 2, 1, 68, 3, 4, 1, 72, 1, 74, 1, 2, 1, 4, 1, 80, 3, 4, 3, 84, 1, 6, 1, 2, 3, 90, 1, 2, 3, 4, 3, 2, 1, 98, 1, 4, 3
Offset: 2
Examples
10 has prime factors 2 and 5, which become 3 and 6 when respectively increased by 1, and gcd(3, 6) = 3. Therefore, a(10) = 3.
Programs
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Mathematica
Table[Apply[GCD, (Transpose[FactorInteger[n]][[1]] + 1)], {n, 2, 100}]