A096847 - OEIS

%I #16 Dec 07 2021 15:20:21

%S 3,4,8,36,100,128,324,400,1296,1600,1936,2116,3364,4356,10404,11236,

%T 20736,22500,26244,27556,28900,30976,38416,40000,52900,53824,57600,

%U 60516,88804,93636,107584,108900,115600,123904,125316,129600,211600

%N Numbers n such that A094471(n) is prime.

%C Old name was "Solutions to {A094471[x]=prime} that is to {x; x*tau[x]-sigma[x]=prime}."

%C All terms after the first are even, because A094471(n) is even if n is odd.  The first term == 2 (mod 4) is a(135) = 9653618. - _Robert Israel_, Nov 11 2015

%H Harvey P. Dale, <a href="/A096847/b096847.txt">Table of n, a(n) for n = 1..100</a>

%e n=8: 8*tau[8]-sigma[8]=8*4-15=32-15=17 is a prime, so 8 is here.

%p A094471:= n -> n*numtheory:-tau(n) - numtheory:-sigma(n):

%p select(t -> isprime(A094471(t)), 2*[3/2,$1..10^6]); # _Robert Israel_, Nov 11 2015

%t Do[s=n*DivisorSigma[0, n]-DivisorSigma[1, n]; If[PrimeQ[s], Print[{n, s}]; ta[[u]]=n; tb[[u]]=s; u=u+1], {n, 1, 1000000}]; ta

%t Select[Range[215000],PrimeQ[# DivisorSigma[0,#]-DivisorSigma[1,#]]&] (* _Harvey P. Dale_, Dec 07 2021 *)

%o (PARI) isok(n) = isprime(n*numdiv(n)-sigma(n)); \\ _Michel Marcus_, Nov 12 2015

%Y Cf. A094471, A096848.

%K nonn

%O 1,1

%A _Labos Elemer_, Jul 15 2004

%E Name modified by _Tom Edgar_, Nov 12 2015