A302297 Values of A000010(m) such that two or more solutions share the same prime signature.

12, 20, 24, 36, 40, 48, 60, 72, 80, 84, 88, 96, 108, 112, 120, 132, 144, 156, 160, 168, 176, 180, 192, 200, 216, 224, 232, 240, 252, 264, 272, 276, 280, 288, 300, 312, 320, 336, 348, 352, 360, 384, 396, 400, 408, 420, 432, 440, 448, 456, 460, 464, 480, 504, 520, 528, 540

Offset

1,1

Comments

Known terms are divisible by 4^m, m >= 1.

Most, but not all terms are evenly divisible by a preceding term. a(1) = 12, a(2) = 20, a(11) = 88, and a(14) = 112 are examples of terms not divisible by an earlier term.

Links

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

Max Alekseyev, PARI scripts for various problems (see invphi.gp there).

Example

12 is a term since A000010(21) = A000010(26) and the prime signature of 21 and 26 is {1,1}.
20 is a term since A000010(44) = A000010(50) and the prime signature of 44 and 50 is {1,2}.
10 is not a term since the only two solutions A000010(11) and A000010(22) do not share the same prime signature.

Prog

(PARI) signa(n) = {my(f = factor(n)); vecsort(f[, 2]); }
isok(n) = {my(vinv = invphi(n), vinvs = vector(#vinv, k, signa(vinv[k]))); return (#vinvs != #Set(vinvs)); }
lista(nn) = {for (n=1, nn, if (istotient(n) && isok(n), print1(n, ", ")); ); } \\ Michel Marcus, Apr 08 2018

Crossrefs

Complement of A302299 w.r.t. A002202. Cf. A000010.

Sequence in context: A109396 A286004 A055598 * A324332 A035511 A095035

Adjacent sequences: A302294 A302295 A302296 * A302298 A302299 A302300

Keyword

nonn,changed

Author

Torlach Rush, Apr 04 2018

Extensions

More terms from Michel Marcus, Apr 09 2018

Status

approved