A239669 Total number of prime factors counted with multiplicity of prime(n)-1 and prime(n)+1, where prime(n) is the n-th prime.
1, 3, 4, 5, 5, 5, 7, 6, 6, 6, 8, 6, 7, 6, 7, 7, 6, 6, 6, 8, 7, 8, 6, 8, 9, 7, 7, 7, 8, 8, 11, 7, 7, 7, 7, 8, 6, 8, 7, 6, 7, 8, 10, 9, 8, 9, 7, 9, 6, 7, 8, 9, 9, 9, 11, 7, 8, 10, 6, 8, 6, 7, 8, 8, 7, 6, 7, 9, 6, 8, 9, 8, 8, 7, 9, 10, 7, 7, 9, 8, 8, 7, 10, 10
Offset: 1
Keywords
Examples
a(7) = 7 as prime(7) = 17, 17-1 = 2^4 and 17+1 = 2*3^2, so total number of prime factors = 4+3 = 7.
Links
- Chris Boyd, Table of n, a(n) for n = 1..10000
Programs
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PARI
forprime(p=1,500,print1(bigomega(p-1) + bigomega(p+1)", "))
Formula
a(n) = Omega(prime(n)^2 - 1), where Omega is A001222.
Comments