A243373 Numbers m such that k*phi(n) = Sum_{j|n} sigma(j), where k >= 1 is an integer.

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

Offset: 1

Author

Paolo P. Lava, Jun 04 2014

Keywords

• nonn

Comments

a(49) > 10^11. - Hiroaki Yamanouchi, Aug 24 2014

Examples

			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.
		

Links

• Hiroaki Yamanouchi, Table of n, a(n) for n = 1..48

Crossrefs

Cf. A000010, A000203, A221219.

Programs

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);

PARI

isok(n) = (sumdiv(n, d, sigma(d)) % eulerphi(n)) == 0; \\ Michel Marcus, Jun 04 2014

Extensions

a(37)-a(40) from Hiroaki Yamanouchi, Aug 24 2014