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A275985
Least k such that n divides phi(k!) (k > 0).
2
1, 3, 6, 4, 10, 6, 14, 4, 7, 10, 22, 6, 26, 14, 10, 5, 34, 7, 38, 10, 14, 22, 46, 6, 11, 26, 9, 14, 58, 10, 62, 5, 22, 34, 14, 7, 74, 38, 26, 10, 82, 14, 86, 22, 10, 46, 94, 6, 21, 11, 34, 26, 106, 9, 22, 14, 38, 58, 118, 10, 122, 62, 14, 6, 26, 22, 134, 34, 46, 14, 142, 7, 146
OFFSET
1,2
LINKS
FORMULA
From Robert Israel, Aug 15 2016: (Start)
If m and n are coprime then a(m*n) = max(a(m),a(n)).
a(n) <= 2n, with equality iff n is an odd prime.
Suppose p is an odd prime. Then
a(p) = 2p
If 2p+1 is prime then a(p^2) = 2p+1 and a(p^3) = 3p.
Otherwise a(p^2) = 3p and a(p^3) = 4p. (End)
EXAMPLE
a(4) = 4 because 4 divides phi(4!) = 8.
MAPLE
A:= proc(n) option remember;
local F, p, e, t, k;
F:= ifactors(n)[2];
if nops(F)=1 then
p:= F[1][1];
e:= F[1][2];
if p = 2 then
t:= 1; if e=1 then return 3 fi;
else
t:= 0
fi;
for k from 2*p by p do
t:= t + padic:-ordp(k, p);
if t >= e then return k fi;
if isprime(k+1) then
t:= t+padic:-ordp(k, p);
if t >= e then return(k+1) fi;
fi;
od
else
max(seq(procname(t[1]^t[2]), t=F))
fi
end proc:
A(1):= 1:
map(A, [$1..100]); # Robert Israel, Aug 15 2016
MATHEMATICA
With[{ep=Table[{EulerPhi[k!], k}, {k, 200}]}, Table[SelectFirst[ep, Divisible[#[[1]], n]&], {n, 80}]][[All, 2]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, May 22 2018 *)
PROG
(PARI) a(n) = {my(k = 1); while(eulerphi(k!) % n, k++); k; }
CROSSREFS
Cf. A048855.
Sequence in context: A316478 A242224 A294671 * A163294 A168577 A122634
KEYWORD
nonn,look
AUTHOR
Altug Alkan, Aug 15 2016
STATUS
approved