A062590 - OEIS

%I #16 Jun 01 2023 16:19:41

%S 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,

%T 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,

%U 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

%N Variation on A029834: a discrete version of the Mangoldt function. If n is prime then floor(log(prime(n))) else 0.

%H Antti Karttunen, <a href="/A062590/b062590.txt">Table of n, a(n) for n = 1..10000</a>

%F 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

%e a(5) = 2 because the fifth prime is 11, the logarithm of which is 2.397895...

%e a(6) = 0 because 6 is not prime.

%e a(7) = 2 because the seventh prime is 17, the logarithm of which is 2.833213344...

%t Table[Boole[PrimeQ[n]] Floor[Log[Prime[n]]], {n, 105}] (* _Alonso del Arte_, Sep 07 2013 *)

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

%Y Cf. A029834.

%K nonn

%O 1,5

%A _Jason Earls_, Jul 03 2001