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A065149
Composite numbers m such that phi(m)*sigma(m) is divisible by m-1.
1
10, 33, 65, 136, 145, 261, 385, 451, 897, 946, 1281, 1441, 1665, 1729, 2241, 2353, 3585, 5185, 6721, 7201, 8380, 8911, 8961, 11521, 11782, 12673, 12801, 17101, 18241, 20737, 25201, 26625, 26677, 26937, 29697, 29953, 30721, 30889, 32896
OFFSET
1,1
LINKS
FORMULA
(A000010(m)*A000203(m)) mod (m-1) = 0, m is composite.
EXAMPLE
m=136, phi(136)=64, sigma(136)=270, product=17280, quotient=128; for primes the formula holds.
MAPLE
with(numtheory): select(m->modp(phi(m)*sigma(m), m-1)=0 and not isprime(m), [$2..40000]); # Muniru A Asiru, Jun 18 2018
MATHEMATICA
Do[s=EulerPhi[n]*DivisorSigma[1, n]; If[IntegerQ[s/(n-1)]&&!PrimeQ[n], Print[n]], {n, 1, 100000}]
PROG
(PARI) { n=0; for (m=2, 10^9, s=eulerphi(m)*sigma(m); if (s%(m-1) == 0 && !isprime(m), write("b065149.txt", n++, " ", m); if (n==500, return)) ) } \\ Harry J. Smith, Oct 12 2009
(GAP) Filtered([2..40000], m->Phi(m)*Sigma(m) mod (m-1)=0 and not IsPrime(m)); # Muniru A Asiru, Jun 18 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
Labos Elemer, Oct 18 2001
EXTENSIONS
Offset changed from 0 to 1 by Harry J. Smith, Oct 12 2009
STATUS
approved