OFFSET
1,5
COMMENTS
Conjecture: (i) a(n) > 0 for all n > 1, and a(n) = 1 only for n = 2, 3, 4, 29, 70, 105.
(ii) Any integer n > 164 can be written as x + y (x, y > 0) with sigma(x) + sigma(y) prime.
LINKS
Zhi-Wei Sun, Table of n, a(n) for n = 1..10000
EXAMPLE
a(2) = 1 since 2 = 1 + 1 with sigma(1) + phi(1) = 2 prime.
a(29) = 1 since 29 = 1 + 28 with sigma(1) + phi(28) = 13 prime.
a(70) = 1 since 70 = 9 + 61 with sigma(9) + phi(61) = 73 prime.
a(105) = 1 since 105 = 4 + 101 with sigma(4) + phi(101) = 107 prime.
MATHEMATICA
f[n_]:=f[n]=Sum[If[Mod[n, d]==0, d, 0], {d, 1, n}]
a[n_]:=a[n]=Sum[If[PrimeQ[f[k]+EulerPhi[n-k]], 1, 0], {k, 1, n/2}]
Table[a[n], {n, 1, 100}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Zhi-Wei Sun, Nov 22 2013
STATUS
approved