

A238263


a(n) is the number of ways n can be written in the form n=2^k1*p1^k2+2^k3*p2^k4, where p1 and p2 are odd prime numbers, and k1, k2, k3, k4 are nonnegative integers.


4



1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 7, 7, 8, 8, 9, 9, 9, 9, 10, 10, 11, 11, 12, 12, 13, 12, 13, 13, 13, 13, 14, 13, 14, 14, 14, 14, 15, 14, 15, 16, 15, 15, 17, 16, 18, 18, 17, 17, 20, 18, 19, 19, 18, 18, 21, 18, 19, 21, 19, 20, 21, 18, 20, 20, 20, 18, 23
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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

Cf. A000961.
Sequence in context: A284849 A274618 A176843 * A071542 A264810 A176841
Adjacent sequences: A238260 A238261 A238262 * A238264 A238265 A238266


KEYWORD

nonn,easy


AUTHOR

Lei Zhou, Feb 21 2014


STATUS

approved



