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.
login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
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
Sequence in context: A047396 A276936 A276937 * A085304 A015843 A109600
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.

License Agreements, Terms of Use, Privacy Policy. .

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