A376927 Totients whose inverses can be separated into ordered pairs (x, 2*x) with no remainder.

1, 6, 10, 18, 22, 28, 30, 42, 46, 52, 54, 58, 66, 70, 78, 82, 100, 102, 106, 110, 126, 130, 136, 138, 148, 150, 162, 166, 172, 178, 180, 190, 196, 198, 210, 222, 226, 228, 238, 250, 262, 268, 270, 282, 292, 294, 306, 310, 316, 330, 342, 346, 348, 358, 366, 372

Offset

1,2

Comments

Conjecture: Numbers having an even number of totient inverses, the odd inverses being confined to the lower half of the list.

Links

Alois P. Heinz, Table of n, a(n) for n = 1..10000

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

Example

1 is a totient and has totient inverses 1 and 2, giving an ordered pair (1, 2*1)
6 is a totient and has totient inverses 7, 9, 14, 18 giving ordered pairs (7,2*7) and (9, 2*9).
18 is a totient and has totient inverses 19, 27, 38, 54 giving ordered pairs (19,2*19) and (27, 2*27).
348 is a totient and has totient inverses 349, 413, 531, 698, 826, 1062 giving ordered pairs (349, 2*349), (413, 2*413), and (531, 2*531).

Maple

q:= n-> (s-> s<>{} and ((x, y)-> x = map(t->t/2, y))(
    selectremove(x-> x::odd, s)))({numtheory[invphi](n)[]}):
select(q, [$1..543])[];  # Alois P. Heinz, Nov 21 2024

Prog

(PARI) evencardinality(list)={e=0; o=0; if(0 < #list, if(0 == Mod(#list, 2), for(i=1, #list, if(1==Mod(list[i], 2), o++, e++)), o++), o++); return(if(o==e, 1, 0))}
for(n = 1, 372, if(1 == evencardinality(invphi(n)), print1(n, ", ")));

Crossrefs

Subset of A002202.

Cf. A000010, A032447.

Sequence in context: A363787 A315361 A315362 * A315363 A301893 A315364

Adjacent sequences: A376924 A376925 A376926 * A376928 A376929 A376930

Keyword

nonn

Author

Torlach Rush, Oct 11 2024

Status

approved