A064439 Numbers n such that sigma(n) - n - 1 = pi(n).

4, 55, 65, 95, 125, 145, 155, 185, 205, 2779, 2863, 55297, 174691, 174779, 487903, 1301989, 1302457, 5254751, 6383483, 23140961, 48267437, 59651051, 70111213, 70111247, 92514491, 199445641, 212210443, 514269523, 514269599, 21881358361, 1602278990111

Offset: 1

Author

Jason Earls, Oct 01 2001

Keywords

• nonn

Comments

a(32) > 3*10^12. - Giovanni Resta, Mar 31 2017

Crossrefs

Cf. A000720, A048050.

Programs

Mathematica

Select[Range[10^5], DivisorSigma[1, #] - # - 1 == PrimePi[#] &] (* Giovanni Resta, Mar 31 2017 *)

PARI

sig(n) = sigma(n)-n-1; pi(x, c=0) = forprime(p=2,x,c++); c for(n=1,10^8, if(sig(n)==pi(n),print(n)))

PARI

{ n=0; for (m=1, 10^9, if ((sigma(m) - m - 1)==primepi(m), write("b064439.txt", n++, " ", m); if (n==100, break)) ) } \\ Harry J. Smith, Sep 14 2009

Extensions

More terms from Klaus Brockhaus, Oct 05 2001. No further term < 800000.

a(16)-a(17) from Harry J. Smith, Sep 14 2009

a(18)-a(29) from Donovan Johnson, Feb 09 2013

a(30)-a(31) from Giovanni Resta, Mar 31 2017