A226230 -id:A226230 - cp's OEIS frontend

A226231 Nontrivial prime powers (A025475) which are a sum of a smaller nontrivial prime power and a perfect square in more than 1 way.

25, 125, 512, 3125, 4913, 50653, 78125, 7645373, 48828125, 69343957, 310288733, 410338673, 1220703125, 4103684801, 24820429213, 164296466333, 296709280757, 762939453125, 1772000266301, 10368641602001, 11392143817501, 19073486328125, 29724740184833, 72079590632113

Offset: 1

Alex Ratushnyak, May 31 2013

nonn

Subsequence of A226230.

			125 = 4 + 11^2 = 25 + 10^2 = 121 + 4^2. Because there are three representations, 125 is in the sequence. Note that 100 + 5^2 is not listed, because 100 is not a prime power.

Cf. A025475, A226230, A226232.

#include 
#include 
#include 
#define TOP (1ULL<<32)
typedef unsigned long long U64;
int compare64(const void *p1, const void *p2) {
  if (*(U64*)p1== *(U64*)p2) return 0;
  return (*(U64*)p1 < *(U64*)p2) ? -1 : 1;
}
int main() {
  U64 i, j, k, p, t, r, n=0, *pp = (U64*)malloc(TOP/2);
  unsigned char *c = (unsigned char *)malloc(TOP/8);
  memset(c, 0, TOP/8);
  for (pp[n++] = i = 1; i < TOP; i+=2)
    if ((c[i>>4] & (1<<((i>>1) & 7)))==0) {
      for (p=i+(i==1), j = p*p; ; j*=p) {
        pp[n++] = j;
        double k = ((double)j) * ((double)p);
        if (k >= ((double)(1ULL<<62)*4.0)) break;
      }
      if(i>1) for (j=i*i>>1; j>3]|= 1<<(j&7);
    }
  qsort(pp, n, 8, compare64);
  for (i = 0; i < n; i++)
    for (p=pp[i], j = k = 0; j < i; j++) {
      t = p - pp[j];
      r = sqrt(t);
      if (r*r==t && ++k==2) { printf("%llu, ", p); break; }
    }
  return 0;
}

A226232 Nontrivial prime powers (A025475) which are a sum of a smaller nontrivial prime power and a perfect cube.

Original entry on oeis.org

9, 16, 128, 243, 512, 841, 1024, 1849, 5041, 6561, 8192, 32041, 65536, 76729, 157609, 177147, 187489, 310249, 524288, 734449, 1104601, 4108729, 4194304, 4782969, 5067001, 7778521, 11498881, 12823561, 31956409, 33554432, 38651089, 65302561, 78552769, 90459121, 129140163

Offset: 1

Alex Ratushnyak, May 31 2013

nonn

Cf. A025475, A226230, A226231.

for n from 1 do
    if isA025475(n) then
        for j from 1 do
            pj := n-j^3 ;
            if pj < 0 then
                break;
            elif isA025475(pj) then
                printf("%d,\n",n);
                break ;
            end if;
        end do:
    end if:
end do: # R. J. Mathar, Jun 06 2013

cp's OEIS Frontend

A226231 Nontrivial prime powers (A025475) which are a sum of a smaller nontrivial prime power and a perfect square in more than 1 way.

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