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A065148
Nonprimes m such that phi(m)*sigma(m) is divisible by m+1.
1
15, 20, 35, 95, 104, 143, 207, 255, 287, 319, 323, 464, 539, 650, 890, 899, 1023, 1034, 1199, 1295, 1349, 1407, 1519, 1763, 1952, 2015, 2204, 2834, 2975, 3599, 4031, 4454, 4607, 5183, 6479, 9215, 9503, 9799, 10403, 11339, 11663, 12095, 12824, 13055
OFFSET
1,1
LINKS
FORMULA
A000010(m)*A000203(m) == 0 (mod m+1), m is composite.
(Every prime p satisfies A000010(p)*A000203(p) == 0 (mod p+1).)
EXAMPLE
m=95, phi(95)=72, sigma(95)=120, product=8640, product/(m+1)=90.
MATHEMATICA
Do[s=EulerPhi[n]*DivisorSigma[1, n]; If[IntegerQ[s/(n+1)]&&!PrimeQ[n], Print[n]], {n, 1, 100000}]
Select[Range[14000], !PrimeQ[#]&&Divisible[EulerPhi[#]DivisorSigma[1, #], #+1]&] (* Harvey P. Dale, Jul 08 2017 *)
PROG
(PARI) { n=0; for (m=1, 10^9, s=eulerphi(m)*sigma(m); if (s%(m+1) == 0 && !isprime(m), write("b065148.txt", n++, " ", m); if (n==500, return)) ) } \\ Harry J. Smith, Oct 12 2009
CROSSREFS
KEYWORD
nonn
AUTHOR
Labos Elemer, Oct 18 2001
EXTENSIONS
Offset changed from 0 to 1 by Harry J. Smith, Oct 12 2009
Definition clarified by Harvey P. Dale, Jul 08 2017
STATUS
approved