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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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Robert Israel, Table of n, a(n) for n = 1..10000 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 Adjacent sequences: A275982 A275983 A275984 * A275986 A275987 A275988 KEYWORD nonn,look AUTHOR Altug Alkan, Aug 15 2016 STATUS approved

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Last modified September 16 22:04 EDT 2024. Contains 375979 sequences. (Running on oeis4.)