A327609 Numbers expressible as a^b + c^d with b&d > 1 and a&c >= 0.

0, 1, 2, 4, 5, 8, 9, 10, 12, 13, 16, 17, 18, 20, 24, 25, 26, 27, 28, 29, 31, 32, 33, 34, 35, 36, 37, 40, 41, 43, 44, 45, 48, 49, 50, 52, 53, 54, 57, 58, 59, 61, 63, 64, 65, 68, 72, 73, 74, 76, 80, 81, 82, 85, 89, 90, 91, 96, 97, 98, 100, 101, 104, 106, 108, 109, 113, 116, 117

Offset: 1

Author

Elan Roth, Sep 18 2019

Keywords

• nonn

Crossrefs

Cf. A070049.

Programs

Mathematica

mx = 120; s = {0,1} ~Join~ Select[Range[2, mx], GCD @@ (Last /@ FactorInteger[#]) > 1 &]; Union[ Reap[Do[v = s[[i]] + s[[j]]; If[v <= mx, Sow@v], {i, Length@s}, {j, i}]][[2, 1]]] (* Giovanni Resta, Sep 19 2019 *)

PARI

upto(n)={my(p=(1 + x + sum(k=2, sqrtint(n), sum(e=2, logint(n,k), x^(k^e))) + O(x*x^n))^2); select(i->polcoef(p,i), [0..n])} \\ Andrew Howroyd, Sep 22 2019