OFFSET
1,6
COMMENTS
Conjecture: a(n) > 0 for all n > 3.
We have verified this for n up to 1.3*10^8.
LINKS
Zhi-Wei Sun, Table of n, a(n) for n = 1..10000
EXAMPLE
a(4) = 1 since 4 = 2 + phi(1^2) + 1*2/2.
a(5) = 1 since 5 = 2 + phi(2^2) + 1*2/2.
a(8) = 1 since 8 = 2^2 + phi(1^2) + 2*3/2.
a(36) = 2 since 36 = 2 + phi(3^2) + 7*8/2 = 2^5 + phi(1^2) + 2*3/2.
MATHEMATICA
f[n_]:=EulerPhi[n^2]
TQ[n_]:=n>0&&IntegerQ[Sqrt[8n+1]]
Do[r=0; Do[If[f[x]>=n, Goto[aa]]; Do[If[TQ[n-f[x]-2^y], r=r+1], {y, 1, Log[2, n-f[x]]}]; Label[aa]; Continue, {x, 1, n}]; Print[n, " ", r]; Continue, {n, 1, 100}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Zhi-Wei Sun, Oct 06 2015
STATUS
approved