A266165 Numbers k such that k = 2*phi(sigma((k-1)/2)) + 1.

3, 5, 17, 25, 257, 481, 1441, 13825, 65537, 285121, 1425601, 2280961, 2380801, 6690817, 7142401, 11404801, 29719873, 59439745, 100638721, 237758977, 4294967297, 7778073601, 8778792961, 43893964801, 94832640001, 184354652161, 266290053121, 663828480001, 921773260801, 1331450265601

Offset

1,1

Comments

Prime terms are in A260476.

The first 5 known Fermat primes from A019434 are in the sequence.

100638721, 8778792961 and 184354652161 are also terms.

Links

Table of n, a(n) for n=1..30.

Formula

a(n) = 2 * A001229(n) + 1. - Max Alekseyev, Nov 15 2025

Example

17 = 2*phi(sigma((17-1)/2)) + 1 = 2*phi(15) + 1 = 2*8 + 1, so 17 is in the sequence.

Mathematica

Select[Range[10000],  # == 2*EulerPhi[DivisorSigma[1, (# - 1)/2] ] + 1 &] (* G. C. Greubel, Dec 22 2015 *)

Prog

(Magma) [n: n in [3..10^7] | n eq 2*EulerPhi(SumOfDivisors((n-1) div 2)) + 1];
(Perl) use ntheory ":all"; for (1..1e7) { say if 2*euler_phi(divisor_sum(($_-1)>>1))+1 == $_ } # Dana Jacobsen, Dec 27 2015
(PARI) is(n)=n%2 && n>2 && 2*eulerphi(sigma((n-1)/2)) + 1 == n \\ Charles R Greathouse IV, Apr 25 2016

Crossrefs

Cf. A000010, A001229, A062401, A260476.

Sequence in context: A024867 A025111 A253204 * A281622 A256439 A256444

Adjacent sequences: A266162 A266163 A266164 * A266166 A266167 A266168

Keyword

nonn

Author

Jaroslav Krizek, Dec 22 2015

Extensions

a(16)-a(23) from Dana Jacobsen, Dec 27 2015

a(24)-a(30) computed from A001229 by Max Alekseyev, Nov 16 2025

Status

approved