A064159 Numbers n such that g(n) + sopfr(n) = n, where g(n)= number of nonprimes <=n (A062298) and sopfr(n) = sum of primes dividing n with repetition (A001414).

1, 24, 27, 30, 55, 65, 95, 145, 155, 185, 205, 822, 894, 2779, 2863, 8104, 64270, 174691, 174779, 1301989, 1302457, 3523478, 9554955, 9555045, 9556455, 70111213, 70111247, 514269523, 514269599, 10246934786, 10246934962, 204475046525, 554805817358, 4086199294828

Offset: 1

Author

Jason Earls, Sep 15 2001

Keywords

• nonn

Comments

That is, numbers n such that primepi(n) = sopfr(n). - Michel Marcus, Mar 25 2017

Programs

Maple

with(numtheory):
a:= proc(n) option remember; local k;
       for k from 1+ `if`(n=1, 0, a(n-1))
       while add(i[1]*i[2], i=ifactors(k)[2])<>pi(k) do od; k
    end:
seq(a(n), n=1..17);  # Alois P. Heinz, Dec 18 2011

Mathematica

a[n_] := a[n] = Module[{k}, For[k = 1 + If[n==1, 0, a[n-1]], Sum[i[[1]] * i[[2]], {i, FactorInteger[k]}] != PrimePi[k], k++]; k]; a[1] = 1;
Table[Print["a(", n, ") = ", a[n]]; a[n], {n, 1, 25}] (* Jean-François Alcover, Mar 25 2017, after Alois P. Heinz *)

PARI

sopfr(n) = my(fac=factor(n)); sum(i=1, #fac~, fac[i,1]*fac[i,2]);
for (n=1,10^6, if (sopfr(n)==primepi(n), print1(n, ", "))) \\ edited by Michel Marcus, Mar 25 2017

Extensions

a(17)-a(21) from Alois P. Heinz, Dec 18 2011

a(22)-a(31) from Donovan Johnson, Jun 29 2012

a(32)-a(34) from Giovanni Resta, Mar 28 2017