A380447 Number of primes dividing n plus n times the number of nonprimes dividing n.
1, 3, 4, 9, 6, 14, 8, 25, 19, 22, 12, 50, 14, 30, 32, 65, 18, 74, 20, 82, 44, 46, 24, 146, 51, 54, 82, 114, 30, 153, 32, 161, 68, 70, 72, 254, 38, 78, 80, 242, 42, 213, 44, 178, 182, 94, 48, 386, 99, 202, 104, 210, 54, 326, 112, 338, 116, 118, 60, 543, 62, 126, 254, 385, 132, 333, 68, 274, 140, 353, 72, 722, 74, 150, 302, 306, 156, 393, 80, 642, 325, 166
Offset: 1
Examples
12 has 2 prime divisors and 4 nonprime divisors, so a(12) = (2) + 12*(4) = 50.
Programs
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Mathematica
Table[n*DivisorSigma[0, n] - (n - 1) PrimeNu[n], {n, 100}]
Formula
a(n) = n*tau(n) - (n-1)*omega(n).
a(n) = Sum_{d|n} n^c(d), where c = A005171.
a(n) = Sum_{d|n} A385313(d).
a(p^k) = 1 + k*p^k for p prime and k>=1. - Wesley Ivan Hurt, Jul 02 2025
Comments