A302299 Values of A000010(m) such that no solutions share the same prime signature.

1, 2, 4, 6, 8, 10, 16, 18, 22, 28, 30, 32, 42, 44, 46, 52, 54, 56, 58, 64, 66, 70, 78, 82, 92, 100, 102, 104, 106, 110, 116, 126, 128, 130, 136, 138, 140, 148, 150, 162, 164, 166, 172, 178, 184, 190, 196, 198, 204, 208, 210, 212, 220, 222, 226, 228, 238, 250, 256, 260

Offset

1,2

Links

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

Max Alekseyev, PARI/GP Scripts for Miscellaneous Math Problems (see invphi.gp there).

Example

1 is a term as the only solutions A000010(1) and A000010(2) do not share the same prime signature.
2 is a term as the only solutions A000010(3), A000010(4), and A000010(6) do not share the same prime signature.
12 is not a term since A000010(21) = A000010(26) are solutions and the prime signature of 21 and 26 is {1,1}.

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 A302297 w.r.t. A002202.

Cf. A000010.

Sequence in context: A102470 A057195 A088007 * A227992 A175299 A088008

Adjacent sequences: A302296 A302297 A302298 * A302300 A302301 A302302

Keyword

nonn,changed

Author

Torlach Rush, Apr 04 2018

Extensions

More terms from Michel Marcus, Apr 09 2018

Status

approved