A062982 Numbers n such that Mertens's function of n (A002321) is divisible by phi(n).

1, 2, 39, 40, 58, 65, 93, 101, 145, 149, 150, 159, 160, 163, 164, 166, 214, 231, 232, 235, 236, 238, 254, 329, 331, 332, 333, 353, 355, 356, 358, 362, 363, 364, 366, 393, 401, 403, 404, 405, 407, 408, 413, 414, 419, 420, 422, 423, 424, 425, 427, 428, 537

Offset

1,2

Comments

Except for the initial term, this sequence is the same as A028442, the n for which Mertens's function M(n) is zero. Because phi(n) >= sqrt(n) and M(n) < sqrt(n) for all known n, phi(n) does not divide M(n), except possibility for some extremely large n. Research project: find the least n > 1 with M(n) not zero and phi(n) divides M(n). - T. D. Noe, Jul 28 2005

Links

Harry J. Smith, Table of n, a(n) for n = 1..1000

Eric Weisstein's World of Mathematics, Mertens Conjecture

Mathematica

Select[Range[500], Mod[Plus @@ MoebiusMu[Range[#]], EulerPhi[#]] == 0 &] (* Carl Najafi, Aug 17 2011 *)

Prog

(PARI) M(n)=sum(k=1, n, moebius(k)); j=[]; for(n=1, 1500, if(Mod(M(n), eulerphi(n))==0, j=concat(j, n))); j
(PARI) { n=m=0; for (k=1, 10^9, m+=moebius(k); if (m%eulerphi(k)==0, write("b062982.txt", n++, " ", k); if (n==1000, break)) ) } \\ Harry J. Smith, Aug 15 2009

Crossrefs

Cf. A002321.

Sequence in context: A055689 A345316 A028442 * A042801 A078733 A201360

Adjacent sequences: A062979 A062980 A062981 * A062983 A062984 A062985

Keyword

nonn

Author

Jason Earls, Jul 25 2001

Status

approved