A225104 Numbers that can be represented as a sum of two distinct nontrivial prime powers in three or more ways.

370, 650, 2210, 3770, 5330, 6290, 7202, 10370, 10730, 11570, 12410, 12818, 13130, 14690, 15170, 15650, 16250, 16490, 18122, 18530, 19370, 19610, 21170, 22490, 24050, 24650, 25010, 26690, 28730, 29930, 30290, 30770, 31610, 32810, 33410, 34970, 36482, 36490

Offset

1,1

Comments

Indices of terms bigger than 2 in A225099.

Nontrivial prime powers are numbers of the form p^k where p is a prime number and k >= 2. That is, A025475 except the first term A025475(1) = 1.

It appears that all terms less than 2^34 are even.

Links

Alois P. Heinz, Table of n, a(n) for n = 1..600

Maple

isA025475not1 := proc(n)
    if n <= 1 then
        false;
    elif isprime(n) then
        false;
    elif nops(numtheory[factorset](n)) = 1 then
        true;
    else
        false;
    end if;
end proc:
A025475not1 := proc(n)
    option remember;
    local a;
    if n = 1 then
        4;
    else
        for a from procname(n-1)+1 do
            if isA025475not1(a) then
                return a;
            end if;
        end do:
    end if;
end proc:
A225104w := proc(n)
    local a, i, ppi, ppj ;
    a := 0 ;
    for i from 1 do
        ppi := A025475not1(i) ;
        if ppi >= n/2 then
            break;
        end if;
        ppj := n-ppi ;
        if isA025475not1(ppj) then
            a := a+1 ;
        end if;
    end do:
    a ;
end proc:
for n from 1 do
    if A225104w(n) >= 3 then
        print(n) ;
    end if;
end do: # R. J. Mathar, Jun 13 2013

Mathematica

nn = 36490; p = Sort[Flatten[Table[Prime[n]^i, {n, PrimePi[Sqrt[nn]]}, {i, 2, Log[Prime[n], nn]}]]]; Transpose[Sort[Select[Tally[Flatten[Table[p[[i]] + p[[j]], {i, Length[p] - 1}, {j, i + 1, Length[p]}]]], #[[1]] <= nn && #[[2]] > 2 &]]][[1]] (* T. D. Noe, Apr 29 2013 *)

Crossrefs

Cf. A025475, A225099, A225102, A225103.

Sequence in context: A276413 A161020 A102618 * A234985 A264895 A283359

Adjacent sequences: A225101 A225102 A225103 * A225105 A225106 A225107

Keyword

nonn

Author

Alex Ratushnyak, Apr 28 2013

Status

approved