A249397 Composite numbers whose Euler totient divides the sum of the Euler totients of the numbers less than or equal to n and not relatively prime to n.
161, 171, 895, 1337, 1843, 1967, 2575, 5833, 8255, 36121, 54439, 87353, 195921, 274115, 284419, 340363, 368449, 387087, 444639, 504539
Offset: 1
Examples
Numbers not coprime to 161 are 7, 14, 21, 23, 28, 35, 42, 46, 49, 56, 63, 69, 70, 77, 84, 91, 92, 98, 105, 112, 115, 119, 126, 133, 138, 140, 147, 154, 161 and the sum of their Euler totients is 1320; phi(161) = 132 and 1320/132 = 10.
Programs
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Maple
with(numtheory): P:=proc(q) local a,k,n; for n from 1 to q do if not isprime(n) then a:=0; for k from 1 to n do if gcd(k,n)>1 then a:=a+phi(k); fi; od; if type(a/phi(n),integer) then print(n); fi; fi; od; end: P(10^9);
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PARI
isok(n) = (n!=1) && !isprime(n) && (sum(k=1, n-1, if (gcd(k, n) != 1, eulerphi(k), 0)) % eulerphi(n) == 0); \\ Michel Marcus, Oct 29 2014
Extensions
a(11)-a(12) from Michel Marcus, Nov 01 2014
a(13)-a(19) from Michel Marcus, Nov 03 2014
a(20) from Ray Chandler, Nov 04 2014
Comments