|
%I #25 Mar 28 2021 12:03:00
%S 15,20,35,95,104,143,207,255,287,319,323,464,539,650,890,899,1023,
%T 1034,1199,1295,1349,1407,1519,1763,1952,2015,2204,2834,2975,3599,
%U 4031,4454,4607,5183,6479,9215,9503,9799,10403,11339,11663,12095,12824,13055
%N Nonprimes m such that phi(m)*sigma(m) is divisible by m+1.
%H Harry J. Smith, <a href="/A065148/b065148.txt">Table of n, a(n) for n = 1..500</a>
%F A000010(m)*A000203(m) == 0 (mod m+1), m is composite.
%F (Every prime p satisfies A000010(p)*A000203(p) == 0 (mod p+1).)
%e m=95, phi(95)=72, sigma(95)=120, product=8640, product/(m+1)=90.
%t Do[s=EulerPhi[n]*DivisorSigma[1, n]; If[IntegerQ[s/(n+1)]&&!PrimeQ[n], Print[n]], {n, 1, 100000}]
%t Select[Range[14000],!PrimeQ[#]&&Divisible[EulerPhi[#]DivisorSigma[1,#],#+1]&] (* _Harvey P. Dale_, Jul 08 2017 *)
%o (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
%Y Cf. A000010, A000203, A062354, A011257.
%K nonn
%O 1,1
%A _Labos Elemer_, Oct 18 2001
%E Offset changed from 0 to 1 by _Harry J. Smith_, Oct 12 2009
%E Definition clarified by _Harvey P. Dale_, Jul 08 2017
|
