OFFSET
1,1
COMMENTS
Conjecture: a(n) exists for any n > 0.
This is motivated by Golomb's result that for any n > 1 there is a positive integer m with mn/pi(mn) = n (i.e., pi(mn) = m).
LINKS
S. W. Golomb, On the Ratio of N to pi(N), American Mathematical Monthly, 69 (1962), 36-37.
Zhi-Wei Sun, A new theorem on the prime-counting function, arXiv:1409.5685, 2014.
EXAMPLE
a(3) = 13 since pi(3*13) = 12 = phi(13).
MATHEMATICA
Do[m=1; Label[aa]; If[PrimePi[n*m]==EulerPhi[m], Print[n, " ", m]; Goto[bb]]; m=m+1; Goto[aa];
Label[bb]; Continue, {n, 1, 18}]
Table[m = 1;
While[PrimePi[n*m] != EulerPhi[m], m++]; m, {n, 1, 12}] (* Robert Price, Sep 08 2019 *)
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Zhi-Wei Sun, Sep 21 2014
EXTENSIONS
a(19)-a(25) from Hiroaki Yamanouchi, Oct 04 2014
STATUS
approved