1,2

All integers of the form p^p*q^q, with q and p two distinct primes, are in the sequence. [R. J. Mathar, Sep 26 2009]

{n: A003415(n) = 2*n}.

For k =84375 = 3^3*5^5, so A003415(k)/2 = 84375*(3/3+5/5)/2 = 84375 = k, which adds k=84375 to the sequence.

P:= proc(p) local a, b, m, n, i, ok, t1, t2, t3; a:=0; for n from 0 by 1 to p do

b:=1000000000039; ok:=0; if n<=1 then a:=0; ok:=1; fi; if isprime(n) then a:=1; ok:=1; fi; if ok=0 then t1:=ifactor(b*n); m:=nops(t1); t2:=0; for i from 1 to m do t3:=op(i, t1); if nops(t3)=1 then t2:=t2+1/op(t3); else t2:=t2+op(2, t3)/op(op(1, t3)); fi; od;

t2:=t2-1/b; a:=n*t2; fi; if a=2*n then lprint(n, a); fi; od; end: P(100000);

Cf. A003415

Sequence in context: A083469 A056001 A163725 this_sequence A155871 A120668 A053526

Adjacent sequences: A165555 A165556 A165557 this_sequence A165559 A165560 A165561

more,nonn

Paolo P. Lava & Giorgio Balzarotti (ppl(AT)spl.at), Sep 22 2009

Entries checked by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Sep 26 2009