A062590 Variation on A029834: a discrete version of the Mangoldt function. If n is prime then floor(log(prime(n))) else 0.
0, 1, 1, 0, 2, 0, 2, 0, 0, 0, 3, 0, 3, 0, 0, 0, 4, 0, 4, 0, 0, 0, 4, 0, 0, 0, 0, 0, 4, 0, 4, 0, 0, 0, 0, 0, 5, 0, 0, 0, 5, 0, 5, 0, 0, 0, 5, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 5, 0, 5, 0, 0, 0, 0, 0, 5, 0, 0, 0, 5, 0, 5, 0, 0, 0, 0, 0, 5, 0, 0, 0, 6, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 6, 0, 6, 0, 0
Offset: 1
Keywords
Examples
a(5) = 2 because the fifth prime is 11, the logarithm of which is 2.397895... a(6) = 0 because 6 is not prime. a(7) = 2 because the seventh prime is 17, the logarithm of which is 2.833213344...
Links
- Antti Karttunen, Table of n, a(n) for n = 1..10000
Crossrefs
Cf. A029834.
Programs
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Mathematica
Table[Boole[PrimeQ[n]] Floor[Log[Prime[n]]], {n, 105}] (* Alonso del Arte, Sep 07 2013 *) -
PARI
v=[]; for(n=1,150,v=concat(v, if(isprime(n),floor(log(prime(n))),))); v
Formula
a(n) = delta(tau(n), 2) * floor(log(prime(n))) = A010051(n) * A029835(n), where delta is the Kronecker delta function and tau is the number of divisors function. - Alonso del Arte, Sep 11 2013