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

0,2

Comments

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

Links

Table of n, a(n) for n=0..28.

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 *)

Prog

(C)
#include <stdio.h>
#include <stdlib.h>
#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;
}

Crossrefs

Cf. A225099.

Sequence in context: A329859 A216381 A085331 * A058040 A130164 A144973

Adjacent sequences: A225097 A225098 A225099 * A225101 A225102 A225103

Keyword

nonn

Author

Alex Ratushnyak, Apr 27 2013

Status

approved