

A233566


a(n) = {0 < p < n: p and p*phi(np)  1 are both prime}, where phi(.) is Euler's totient function (A000010).


7



0, 0, 0, 1, 2, 2, 2, 2, 2, 4, 3, 3, 4, 4, 3, 3, 2, 2, 4, 3, 3, 5, 5, 4, 5, 3, 2, 6, 2, 4, 2, 7, 7, 8, 5, 4, 8, 4, 4, 8, 5, 5, 8, 4, 4, 5, 6, 5, 5, 10, 7, 8, 4, 4, 5, 6, 8, 7, 4, 6, 6, 9, 11, 7, 10, 4, 6, 7, 8, 10, 4, 7, 6, 5, 5, 12, 8, 8, 7, 11, 13, 11, 12, 5, 8, 7, 11, 9, 5, 8, 5, 6, 12, 8, 8, 5, 9, 5, 11, 12
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,5


COMMENTS

Conjecture: a(n) > 0 for all n > 3. Also, for any n > 2 there is a prime p < n with p^2*phi(np)  1 prime.


LINKS



EXAMPLE

a(4) = 1 since 3 and 3*phi(43)  1 = 2 are both prime.
a(5) = 2 since 2 and 2*phi(52)  1 = 3 are both prime, and also 3 and 3*phi(53)  1 = = 2 are both prime.


MATHEMATICA

a[n_]:=Sum[If[PrimeQ[Prime[k]*EulerPhi[nPrime[k]]1], 1, 0], {k, 1, PrimePi[n1]}]
Table[a[n], {n, 1, 100}]


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



