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A227644 Perfect powers equal to the sum of 2 factorial numbers. 9
4, 8, 25, 121, 144, 5041 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

a(7), if it exists, is greater than 10^100.

a(7), if it exists, is greater than 10000!. - Filip Zaludek, Jul 18 2017

a(7), if it exists, is greater than 11750!. - Filip Zaludek, Sep 07 2018

LINKS

Table of n, a(n) for n=1..6.

Giovanni Resta, Decompositions of a(1)-a(6)

EXAMPLE

5041 = 71^2 = 1! + 7!.

PROG

(C)

/* To compile: gcc -Wall -O2 A227644.c -o A227644 -lgmp */

#include <stdio.h>

#include <stdlib.h>

#include <gmp.h>

int main()

{

   int bsz=256, a=0;

   mpz_t *f, t;

   f = malloc(sizeof(mpz_t) * bsz);

   mpz_init(t); mpz_init(f[0]); mpz_set_ui(f[0], 1);

   while (1)

   {

       a += 1;

       if (a == bsz)

       {

           bsz *= 2;

           f = (mpz_t *) realloc(f, sizeof(mpz_t) * bsz);

       }

       mpz_init(f[a]);

       mpz_mul_ui(f[a], f[a-1], a);

       for (int i=1; i<=a; i++)

       {

           mpz_add(t, f[a], f[i]);

           if (mpz_perfect_power_p(t))

           {

               gmp_printf("%Zd, ", t);

               fflush(stdout);

           }

       }

   }

   return 0;

}

CROSSREFS

Cf. A114377, A227645, A227646, A227647, A227648, A227649, A227650, A227651, A065433, A085692.

Sequence in context: A046736 A174171 A262042 * A074188 A126733 A297695

Adjacent sequences:  A227641 A227642 A227643 * A227645 A227646 A227647

KEYWORD

nonn,more

AUTHOR

Giovanni Resta, Jul 19 2013

STATUS

approved

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Last modified July 23 16:14 EDT 2019. Contains 325258 sequences. (Running on oeis4.)