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

1,5

Links

Antti Karttunen, Table of n, a(n) for n = 1..10000

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

Example

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...

Mathematica

Table[Boole[PrimeQ[n]] Floor[Log[Prime[n]]], {n, 105}] (* Alonso del Arte, Sep 07 2013 *)

Prog

(PARI) v=[]; for(n=1, 150, v=concat(v, if(isprime(n), floor(log(prime(n))), ))); v

Crossrefs

Cf. A029834.

Sequence in context: A050948 A282695 A292936 * A139215 A139216 A348692

Adjacent sequences: A062587 A062588 A062589 * A062591 A062592 A062593

Keyword

nonn

Author

Jason Earls, Jul 03 2001

Status

approved