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

Author

Alex Ratushnyak, Apr 28 2013

Keywords

• nonn

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

Crossrefs

Cf. A025475, A225099, A225102, A225103.

Programs

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 *)