The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A243373 Numbers m such that k*phi(n) = Sum_{j|n} sigma(j), where k >= 1 is an integer. 1
 1, 2, 6, 9, 10, 14, 18, 26, 42, 66, 90, 126, 150, 186, 234, 266, 342, 490, 666, 1426, 1634, 2394, 4410, 12834, 14706, 16758, 18846, 209754, 308602, 350154, 385434, 1122786, 2777418, 12130734, 15616986, 29682342, 223843466, 270397974, 300398714, 559894482 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS a(49) > 10^11. - Hiroaki Yamanouchi, Aug 24 2014 LINKS Hiroaki Yamanouchi, Table of n, a(n) for n = 1..48 EXAMPLE The divisors of 90 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90 and sigma(1) + sigma(2) + sigma(3) + sigma(5) + sigma(6) + sigma(9) + sigma(10) + sigma(15) + sigma(18) + sigma(30) + sigma(45) + sigma(90) = 1 + 3 + 4 + 6 + 12 + 13 + 18 + 24 + 39 + 72 + 78 + 234 = 504 and phi(n) = 24. Finally 504 / 24 = 21. MAPLE with(numtheory): P:=proc(q) local a, b, k, n; for n from 1 to q do a:=divisors(n); b:=0; b:=add(sigma(a[k]), k=1..nops(a)); if type(b/phi(n), integer) then print(n); fi; od; end: P(10^10); PROG (PARI) isok(n) = (sumdiv(n, d, sigma(d)) % eulerphi(n)) == 0; \\ Michel Marcus, Jun 04 2014 CROSSREFS Cf. A000010, A000203, A221219. Sequence in context: A047396 A276936 A276937 * A085304 A015843 A109600 Adjacent sequences: A243370 A243371 A243372 * A243374 A243375 A243376 KEYWORD nonn AUTHOR Paolo P. Lava, Jun 04 2014 EXTENSIONS a(37)-a(40) from Hiroaki Yamanouchi, Aug 24 2014 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified May 29 20:00 EDT 2024. Contains 372952 sequences. (Running on oeis4.)