A194568 Numbers k other than powers of 2 such that sigma(k) + 2*phi(k) = sigma(phi(k)) + 2k.

78, 4044, 5064, 294380, 1691586, 8413520, 68121168, 663003222, 966241404, 7675923264, 20555122128, 24443986296

Offset

1,1

Links

Table of n, a(n) for n=1..12.

Formula

{n not in A000079: A033880(n) +2*A000010(n) = A062402(n)}. - R. J. Mathar, Oct 13 2011

Mathematica

Select[Range[300000], # != 2^IntegerExponent[#, 2] && DivisorSigma[1, #] + 2*EulerPhi[#] == DivisorSigma[1, EulerPhi[#]] + 2*# &] (* Amiram Eldar, Dec 08 2023 *)

Prog

(PARI) test(n)=my(p=eulerphi(n)); sigma(n)+2*p==sigma(p)+2*n
for(k=1, 20, for(n=1<<k+1, 2<<k-1, if(test(n), print1(n", ")))) \\ Charles R Greathouse IV, Oct 12 2011

Crossrefs

Cf. A000010, A000079, A000203, A033880, A062402.

Sequence in context: A017741 A060562 A004367 * A276177 A093278 A328354

Adjacent sequences: A194565 A194566 A194567 * A194569 A194570 A194571

Keyword

nonn,more

Author

Naohiro Nomoto, Oct 12 2011

Extensions

a(6)-a(9) from Charles R Greathouse IV, Oct 12 2011

a(10)-a(12) from Amiram Eldar, Dec 08 2023

Status

approved