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 A292024 a(n) is the smallest k such that n divides psi(k!) (k > 0). 1
 1, 3, 2, 3, 10, 3, 13, 4, 5, 10, 22, 3, 26, 13, 10, 4, 34, 5, 37, 10, 13, 22, 46, 4, 15, 26, 6, 13, 58, 10, 61, 5, 22, 34, 13, 5, 73, 37, 26, 10, 82, 13, 86, 22, 10, 46, 94, 4, 14, 15, 34, 26, 106, 6, 22, 13, 37, 58, 118, 10, 122, 61, 13, 6, 26, 22, 134, 34, 46, 13, 142, 5, 146, 73, 15, 37, 22, 26, 157 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS From Robert Israel, Sep 14 2017: (Start) If m and n are coprime then a(m*n) = max(a(m),a(n)). a(n) <= 2n. Suppose p is a prime >= 5. Then a(p) = 2p-1 if p is in A005382, otherwise 2p. a(p^2) = 2p if p is in A005382, otherwise 3p. a(p^3) = 3p if p is in A005382, 4p-1 if p is in A062737, otherwise 4p. (End) LINKS Robert Israel, Table of n, a(n) for n = 1..10000 EXAMPLE a(4) = 3 because 4 divides psi(3!) = 12 and 3 is the least number with this property. 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 = 3 then t:= 1; if e =1 then return 2 fi else t:= 0: fi; for k from 2*p by p do if isprime(k-1) then t:= t+padic:-ordp(k, p); if t >= e then return(k-1) fi; fi; t:= t + padic:-ordp(k, p); if t >= e then return k fi; od else max(seq(procname(t[1]^t[2]), t=F)) fi end proc: A(1):= 1: map(A, [\$1..100]); # Robert Israel, Sep 14 2017 MATHEMATICA psi[n_] := Module[{p, e}, Product[{p, e} = pe; p^e + p^(e-1), {pe, FactorInteger[n]}]]; a[n_] := Module[{k = 1}, While[!Divisible[psi[k!], n], k++]; k]; a[2] = 3; Array[a, 100] (* Jean-François Alcover, Oct 15 2020, after PARI *) PROG (PARI) a001615(n) = my(f=factor(n)); prod(i=1, #f~, f[i, 1]^f[i, 2] + f[i, 1]^(f[i, 2]-1)); a(n) = {my(k=1); while(a001615(k!) % n, k++); k; } \\ after Charles R Greathouse IV at A001615 CROSSREFS Cf. A001615, A005382, A062737, A275985. Sequence in context: A010605 A120879 A118064 * A290093 A186102 A170848 Adjacent sequences: A292021 A292022 A292023 * A292025 A292026 A292027 KEYWORD nonn,look AUTHOR Altug Alkan, Sep 07 2017 STATUS approved

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Last modified November 29 17:22 EST 2023. Contains 367445 sequences. (Running on oeis4.)