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A225100 First occurrence of n in A225099, or -1 if n does not appear in A225099. 1
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 (list; graph; refs; listen; history; text; internal format)
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: A278583 A216381 A085331 * A058040 A130164 A144973

Adjacent sequences:  A225097 A225098 A225099 * A225101 A225102 A225103

KEYWORD

nonn

AUTHOR

Alex Ratushnyak, Apr 27 2013

STATUS

approved

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Last modified May 22 21:17 EDT 2019. Contains 323504 sequences. (Running on oeis4.)