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

1,2

Comments

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

Links

Table of n, a(n) for n=1..34.

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 *)

Prog

(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

Crossrefs

Sequence in context: A116203 A345499 A071833 * A141632 A308603 A141634

Adjacent sequences: A064156 A064157 A064158 * A064160 A064161 A064162

Keyword

nonn

Author

Jason Earls, Sep 15 2001

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

Status

approved