

A302297


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


1



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
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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

Table of n, a(n) for n=1..57.
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


AUTHOR

Torlach Rush, Apr 04 2018


EXTENSIONS

More terms from Michel Marcus, Apr 09 2018


STATUS

approved



