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 A226231 Nontrivial prime powers (A025475) which are a sum of a smaller nontrivial prime power and a perfect square in more than 1 way. 2
 25, 125, 512, 3125, 4913, 50653, 78125, 7645373, 48828125, 69343957, 310288733, 410338673, 1220703125, 4103684801, 24820429213, 164296466333, 296709280757, 762939453125, 1772000266301, 10368641602001, 11392143817501, 19073486328125, 29724740184833, 72079590632113 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Subsequence of A226230. LINKS EXAMPLE 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. PROG (C) #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; } CROSSREFS Cf. A025475, A226230, A226232. Sequence in context: A036321 A289337 A211581 * A211595 A066609 A074006 Adjacent sequences:  A226228 A226229 A226230 * A226232 A226233 A226234 KEYWORD nonn AUTHOR Alex Ratushnyak, May 31 2013 STATUS approved

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Last modified February 16 21:37 EST 2020. Contains 331975 sequences. (Running on oeis4.)