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%I #23 Nov 05 2020 06:48:29
%S 4,8,25,121,144,5041
%N Perfect powers equal to the sum of 2 factorial numbers.
%C a(7), if it exists, is greater than 10^100.
%C a(7), if it exists, is greater than 10000!. - _Filip Zaludek_, Jul 18 2017
%C a(7), if it exists, is greater than 11750!. - _Filip Zaludek_, Sep 07 2018
%C a(7), if it exists, is greater than 20000!. - _Filip Zaludek_, Nov 04 2020
%H Giovanni Resta, <a href="/A227644/a227644.txt">Decompositions of a(1)-a(6)</a>
%e 5041 = 71^2 = 1! + 7!.
%o (C)
%o /* To compile: gcc -Wall -O2 A227644.c -o A227644 -lgmp */
%o #include <stdio.h>
%o #include <stdlib.h>
%o #include <gmp.h>
%o int main()
%o {
%o int bsz=256, a=0;
%o mpz_t *f, t;
%o f = malloc(sizeof(mpz_t) * bsz);
%o mpz_init(t); mpz_init(f[0]); mpz_set_ui(f[0], 1);
%o while (1)
%o {
%o a += 1;
%o if (a == bsz)
%o {
%o bsz *= 2;
%o f = (mpz_t *) realloc(f, sizeof(mpz_t) * bsz);
%o }
%o mpz_init(f[a]);
%o mpz_mul_ui(f[a], f[a-1], a);
%o for (int i=1; i<=a; i++)
%o {
%o mpz_add(t, f[a], f[i]);
%o if (mpz_perfect_power_p(t))
%o {
%o gmp_printf("%Zd, ", t);
%o fflush(stdout);
%o }
%o }
%o }
%o return 0;
%o }
%Y Cf. A114377, A227645, A227646, A227647, A227648, A227649, A227650, A227651, A065433, A085692.
%K nonn,more
%O 1,1
%A _Giovanni Resta_, Jul 19 2013
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