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A389859
Totient numbers k such that A014197(k) divides A215240(k).
3
6, 8, 32, 42, 368, 416, 464, 468, 486, 492, 616, 636, 656, 732, 848, 900, 1092, 1212, 1232, 1288, 1328, 1356, 1360, 1376, 1424, 1472, 1480, 1560, 1568, 1572, 1640, 1664, 1696, 1808, 1896, 2064, 2076, 2144, 2148, 2196, 2208, 2256, 2296, 2328, 2336, 2464, 2480, 2508
OFFSET
1,1
COMMENTS
Numbers k such that the set of solutions to phi(x) = k is not empty and has an integer arithmetic mean.
LINKS
David M. Bressoud, A Course in Computational Number Theory (web page), CNT.m, Computational Number Theory Mathematica package.
EXAMPLE
a(4) = 6 since the 4 solutions to phi(x) = 6 are 7, 9, 14, and 18 and their arithmetic mean, (7 + 9 + 14 + 18)/4 = 12, is an integer.
MATHEMATICA
q[k_] := Module[{s = PhiInverse[k]}, s != {} && Divisible[Total[s], Length[s]]]; Select[2 * Range[1300], q] (* using David M. Bressoud's CNT.m *)
PROG
(PARI) isok(k) = {my(v = invphi(k)); #v > 0 && vecsum(v) % (#v) == 0; } \\ using Max Alekseyev's invphi.gp
CROSSREFS
Cf. A000010 (phi), A002202 (totient numbers), A014197, A215240, A389860.
Sequence in context: A076904 A354205 A219681 * A025091 A356742 A303156
KEYWORD
nonn,easy
AUTHOR
Amiram Eldar, Oct 17 2025
STATUS
approved