OFFSET
1,2
COMMENTS
Consider numbers in the cototient of n, listed in row n of A121998. For composite n > 4, there are nondivisors m in the cototient, listed in row n of A133995. Of these m, there are two species. The first are m that divide n^e with integer e > 1, while the last do not divide n^e. These are listed in row n of A272618 and A272619, and counted by A243822(n) and A243823(n), respectively. This sequence lists the record setters in the sequence A300858(n), which is a function that represents the difference between the latter and the former species of nondivisors in the cototient of n.
Odd terms m < 36,000,000: {1, 15, 27}.
LINKS
Michael De Vlieger, Table of n, a(n) for n = 1..1710
Michael De Vlieger, Decomposition of terms in A300860 and Related Sequences.
EXAMPLE
8 is in the sequence because A300858(n) for n < 8 is negative or 0 after A300858(1) = 0. A300858(8) = A243823(8) - A243822(8) = 1 - 0 = 1. Within the cototient of 8 there is one nondivisor (6) and it does not divide 8^e for integer e. (All prime powers m have A243822(m) = 0 and for m > 4, A243823(m) is positive.)
MATHEMATICA
f[n_] := Count[Range@ n, _?(PowerMod[n, Floor@ Log2@ n, #] == 0 &)]; With[{s = Array[#1 - #3 + 1 - 2 #2 + #4 & @@ {#, f@ #, EulerPhi@ #, DivisorSigma[0, #]} &, 550]}, Map[FirstPosition[s, #][[1]] &, Union@ FoldList[Max, s]] ]
PROG
(PARI) a300858(n) = 1 + n + numdiv(n) - eulerphi(n) - 2*sum(k=1, n, if(gcd(n, k)-1, 0, moebius(k)*(n\k))) \\ after Michel Marcus
r=-1; for(i=1, oo, if(a300858(i) > r, print1(i, ", "); r=a300858(i))) \\ Felix Fröhlich, Mar 30 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
Michael De Vlieger, Mar 14 2018
STATUS
approved