A225102 Numbers that can be represented as a sum of two distinct nontrivial prime powers (numbers of the form p^k where p is a prime number and k >= 2).
12, 13, 17, 20, 24, 25, 29, 31, 33, 34, 35, 36, 40, 41, 43, 48, 52, 53, 57, 58, 59, 65, 68, 72, 73, 74, 76, 80, 81, 85, 89, 90, 91, 96, 97, 106, 108, 113, 125, 129, 130, 132, 133, 134, 136, 137, 141, 144, 145, 146, 148, 150, 152, 153, 155, 157, 160, 170, 173, 174, 177
Offset: 1
Keywords
Links
- Robert Israel, Table of n, a(n) for n = 1..10000
Programs
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C
#include
#include #define TOP (1ULL<<17) unsigned long long *powers, pwFlat[TOP], primes[TOP] = {2}; int main() { unsigned long long a, c, i, j, k, n, p, r, pp = 1, pfp = 0; powers = (unsigned long long*)malloc(TOP * TOP/8); memset(powers, 0, TOP * TOP/8); for (a = 3; a < TOP; a += 2) { for (p = 0; p < pp; ++p) if (a % primes[p] == 0) break; if (p == pp) primes[pp++] = a; } for (k = i = 0; i < pp; ++i) for (j = primes[i]*primes[i]; j < TOP*TOP; j *= primes[i]) powers[j/64] |= 1ULL << (j & 63), ++k; if (k > TOP) exit(1); for (n = 0; n < TOP * TOP; ++n) if (powers[n/64] & (1ULL << (n & 63))) pwFlat[pfp++] = n; for (n = 0; n < TOP * TOP; ++n) { for (c = i = 0; pwFlat[i] * 2 < n; ++i) r=n-pwFlat[i], c+= (powers[r/64] & (1ULL <<(r&63))) > 0; if (c) printf("%llu, ", n); } return 0; } -
Maple
N:= 1000: # to get all terms <= N P:= select(isprime, [2,seq(i,i=3..floor(sqrt(N)),2)]): PP:= sort(map(p -> seq(p^t,t=2..floor(log[p](N))), P)): sort(convert(select(`<=`,{seq(seq(PP[i]+PP[j],j=1..i-1),i=1..nops(PP))},N),list)); # Robert Israel, Feb 21 2017 -
Mathematica
nn = 177; p = Sort[Flatten[Table[Prime[n]^i, {n, PrimePi[Sqrt[nn]]}, {i, 2, Log[Prime[n], nn]}]]]; Select[Union[Flatten[Table[p[[i]] + p[[j]], {i, Length[p] - 1}, {j, i + 1, Length[p]}]]], # <= nn &] (* T. D. Noe, Apr 29 2013 *)
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