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A062590 Variation on A029834: a discrete version of the Mangoldt function. If n is prime then floor(log(prime(n)) else 0. 3
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 (list; graph; refs; listen; history; text; internal format)
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 A300824

Adjacent sequences:  A062587 A062588 A062589 * A062591 A062592 A062593

KEYWORD

nonn

AUTHOR

Jason Earls, Jul 03 2001

STATUS

approved

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Last modified October 18 12:18 EDT 2019. Contains 328160 sequences. (Running on oeis4.)