A068540 Numbers k such that phi(k) = bigomega(k)*tau(k)^2.

5, 51, 171, 357, 442, 582, 1071, 1250, 1292, 1460, 1746, 5456, 6435, 6825, 7248, 8060, 8140, 8540, 9348, 9486, 9516, 9594, 9632, 9636, 10476, 10860, 10950, 12192, 20910, 23160, 23680, 25308, 27468, 28032, 29340, 31392, 34000, 37488, 45220, 49504, 50388, 51680

Offset

1,1

Comments

Conjecture: a(116) = 14137200 is the last term of this sequence (checked up to 10^10). - Amiram Eldar, Jun 24 2022

Since bigomega(k) <= tau(k), we have phi(k) <= tau(k)^3 and finiteness then follows from the same argument as given in A068559. I confirm that the sequence contains 116 terms and thus is complete. - Max Alekseyev, Oct 19 2025

Links

Amiram Eldar, Table of n, a(n) for n = 1..116 (terms 1..100 from Harvey P. Dale)

Mathematica

Select[Range[46000], EulerPhi[#]==PrimeOmega[#]DivisorSigma[0, #]^2&] (* Harvey P. Dale, Jun 06 2021 *)

Crossrefs

Cf. A000005, A000010, A001222, A068559, A068560.

Sequence in context: A117710 A064019 A134938 * A208997 A041043 A362516

Adjacent sequences: A068537 A068538 A068539 * A068541 A068542 A068543

Keyword

nonn,full,fini

Author

Benoit Cloitre, Mar 25 2002

Extensions

Keywords full, fini added by Max Alekseyev, Oct 19 2025

Status

approved