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Search: id:A062982
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| A062982 |
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Numbers n such that Mertens' function of n (A002321) is divisible by phi(n). |
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+0
7
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| 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
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Except for the initial term, this sequence is the same as A028442, the n for which Mertens 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 (noe(AT)sspectra.com), Jul 28 2005
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LINKS
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Harry J. Smith, Table of n, a(n) for n=1,...,1000
Eric Weisstein's World of Mathematics, Mertens Conjecture
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PROGRAM
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(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)) ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Aug 15 2009]
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CROSSREFS
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Cf. A002321.
Sequence in context: A066244 A055689 A028442 this_sequence A042801 A078733 A080920
Adjacent sequences: A062979 A062980 A062981 this_sequence A062983 A062984 A062985
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KEYWORD
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nonn
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AUTHOR
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Jason Earls (zevi_35711(AT)yahoo.com), Jul 25 2001
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