A225100 First occurrence of n in A225099, or -1 if n does not appear in A225099.

0, 12, 36, 370, 3770, 12410, 202130, 197210, 81770, 9151610, 16046810, 12625730, 21899930, 95336930, 9549410, 416392730, 1016275130, 338609570, 789396530, 601741010, 254885930, 10083683090, 4690939370, 29207671610, 30431277890, 22264417370, 23231920010, 10838858810, 37462976330

Offset: 0

Author

Alex Ratushnyak, Apr 27 2013

Keywords

• nonn

Comments

Least integer k representable as a sum of two distinct nontrivial prime powers (A025475 except the first term) in exactly n ways.

Crossrefs

Cf. A225099.

Programs

C

#include 
#include 
#define TOP (5ULL<<16)
typedef unsigned long long U64;
U64 *mem, pwFlat[TOP], primes[TOP]={2}, f[96];
int pp_compare(const void *p1, const void *p2) {
  if (*(U64*)p1 == *(U64*)p2) return 0;
  if (*(U64*)p1 < *(U64*)p2) return -1;
  return 1;
}
int main() {
  U64 i, j, k, p, pp=1, pfp;
  mem = (U64*)malloc(3ULL<<30);
  for (i = 3; i < TOP; i+=2) {
    for (p = 0; p < pp; ++p)  if (i%primes[p] == 0) break;
    if (p==pp)  primes[pp++] = i;
  }
  for (pfp = i = 0; i < pp; ++i)
    for (j = primes[i]*primes[i]; j < TOP*TOP; j *= primes[i])
      pwFlat[pfp++] = j;
  for (k = i = 0; i < pfp; ++i)
    for (j = i+1; j < pfp; ++j)
      if ((p = pwFlat[i] + pwFlat[j]) < TOP*TOP) mem[k++] = p;
  qsort(mem, k, 8, pp_compare);
  p = mem[0];
  for (i = j = mem[k] = 1; i <= k; ++i) {
    if (p == mem[i])  { ++j; continue; }
    if (j < 96 && f[j] == 0)  f[j] = p;
    p = mem[i];
    j = 1;
  }
  for (i = 0; i < 96; ++i)  printf("%llu, ", f[i]);
  return 0;
}

Mathematica

nn = 300000; p = Sort[Flatten[Table[Prime[n]^i, {n, PrimePi[Sqrt[nn]]}, {i, 2, Log[Prime[n], nn]}]]]; t =Sort[Select[Flatten[Table[p[[i]] + p[[j]], {i, Length[p] - 1}, {j, i + 1, Length[p]}]], # <= nn &]]; t2 = Table[Count[t, n], {n, 0, nn}]; n2 = Max[t2]; Table[Position[t2, n, 1, 1][[1, 1]], {n, 0, n2}] - 1(* T. D. Noe, Apr 29 2013 *)