|
%I #25 Sep 24 2019 05:08:16
%S 4,9,25,36,144,441,676,1089,1296,1764,2304,4900,5184,9216,15876,33124,
%T 36100,43264,51984,82944,115600,142884,147456,224676,266256,298116,
%U 331776,389376,467856,898704,944784,1016064,1587600,2286144,3111696
%N Numbers whose sum of non-unitary divisors is a prime and sets a new record for such primes.
%H Amiram Eldar, <a href="/A063760/b063760.txt">Table of n, a(n) for n = 1..100</a> (terms 1..51 from Harry J. Smith)
%e 441 is a term because sigma(441) - usigma(441) = 241, a prime.
%t fun[p_, e_] := (p^(e+1)-1)/(p-1); nusigma[1] = 0; nusigma[n_] := Times @@ (fun @@@ (f = FactorInteger[n])) - Times @@ (1 + Power @@@ f); s = {}; pm = 0; Do[If[ PrimeQ[(p = nusigma[n])] && p > pm, pm = p; AppendTo[s, n] ], {n, 1, 10^5}]; s (* _Amiram Eldar_, Sep 24 2019 *)
%o (PARI) u(n) = sumdiv(n,d, if(gcd(d, n/d)==1,d));
%o a=0; for(n=1,50000,x=sigma(n)-u(n); if(isprime(x),b=x; if(b>a,a=b; print(n))))
%o (PARI) u(n) = sumdiv(n, d, if(gcd(d, n/d)==1, d))
%o { n=-1; a=0; for (m=1, 10^9, if(isprime(b=sigma(m) - u(m)), if(b>a, a=b; write("b063760.txt", n++, " ", m); if (n==50, break))) ) } \\ _Harry J. Smith_, Aug 30 2009
%Y Cf. A048146.
%K nonn
%O 1,1
%A _Jason Earls_, Aug 24 2001
%E Six more terms from _Harry J. Smith_, Aug 30 2009
%E Offset corrected by _Amiram Eldar_, Sep 24 2019
|
