A177204 Pseudoperfect totient numbers (A288452) which are not powers of primes (A000961).

15, 33, 35, 39, 51, 55, 65, 69, 77, 85, 87, 111, 115, 119, 123, 141, 143, 153, 155, 159, 161, 175, 177, 183, 187, 201, 205, 209, 213, 219, 221, 235, 245, 247, 249, 253, 255, 265, 267, 287, 291, 295, 299, 303, 305, 309, 319, 321, 323, 325, 327, 329, 339, 341, 363, 371, 377, 391, 393, 403, 407, 411, 413, 415

Offset: 1

Author

Amiram Eldar and Robert G. Wilson v, Jul 02 2017

Keywords

• nonn
• easy

Comments

A proper subset of A288452. All odd primes and all powers of 3 are pseudoperfect totient numbers. First term which has k factors counting multiplicity >1: 15, 153, 875, 4375, 62451, etc. First term which has k distinct factors >1: 15, 255, 21505, etc.

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A288452, A000961.

Programs

Mathematica

fQ[n_] := Module[{tots = Rest@ NestWhileList[ EulerPhi, n, # > 1 &]}, MemberQ[Total /@ Subsets[tots, Length[ tots]], n]]; Select[ Range[ 3, 440, 2], fQ@# && !PrimePowerQ@# &]