OFFSET
2,3
COMMENTS
Sequence is defined for n >= 2.
When ki=0, corresponding terms 2^k1, p1^k2, 2^k3, or p2^k4 are 1.
All terms of this sequence are greater than zero.
LINKS
Lei Zhou, Table of n, a(n) for n = 2..10000
EXAMPLE
n=2, 2=1*1+1*1. This is the only choice that matches the definition. So a(2)=1;
...
n=37, 37 = 1*1+2^2*3^2 = 1*3+2*17*1 = 1*5+2^5*1 = 2*3*1+1*31 = 2^3*1+1*29 = 1*3^2+2^2*7 = 2*5+1*3^3 = 1*11+2*13 = 2^2*3+1*5^2 = 1*13+2^3*3 = 2*7+1*23 = 1*17+2^2*5 = 2*3^2+1*19, 13 ways matching the definition. So a(37)=13.
MATHEMATICA
Table[ct = 0; Do[If[f1 = FactorInteger[i]; l1 = Length[f1]; If[f1[[1, 1]] == 2, l1--]; f2 = FactorInteger[n - i]; l2 = Length[f2]; If[f2[[1, 1]] == 2, l2--]; (l1 <= 1) && (l2 <= 1), ct++], {i, 1, Floor[n/2]}]; ct, {n, 2, 72}]
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Lei Zhou, Feb 21 2014
STATUS
approved