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 A291674 a(n) is the smallest k such that 2^psi(k) == 2^phi(n) (mod n). 0
 1, 1, 3, 2, 3, 3, 2, 2, 4, 3, 19, 3, 6, 2, 3, 3, 7, 4, 10, 3, 4, 19, 43, 3, 19, 6, 10, 2, 39, 3, 19, 4, 19, 7, 6, 4, 18, 10, 6, 3, 19, 4, 13, 19, 6, 43, 137, 3, 26, 19, 7, 6, 103, 10, 19, 2, 10, 39, 173, 3, 38, 19, 4, 4, 6, 19, 86, 7, 43, 6, 139, 4, 10, 18, 19, 10, 25, 6, 206, 3, 34, 19, 163 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Remainders when 2^phi(n) is divided by n are 0, 0, 1, 0, 1, 4, 1, 0, 1, 6, 1, 4, 1, 8, 1, 0, 1, 10, 1, 16, 1, 12, ... (i.e., the values of "1" come from Euler's totient theorem). If n is odd, a(n) is the least k such that psi(k) is divisible by A002326((n-1)/2). - Robert Israel, Aug 29 2017 LINKS EXAMPLE a(11) = 19 because 2^psi(19) == 2^phi(11) (mod 11) and 19 is the least number with this property. MAPLE N:= 1000: # to get terms before the first term > N Psis:= Vector([\$1..N]): for p in select(isprime, [2, seq(i, i=3..N, 2)]) do   pm:= p*[\$1..N/p];   Psis[pm]:= map(`*`, Psis[pm], 1+1/p); od: for n from 1 do   r:= 2 &^ numtheory:-phi(n) mod n;   for k from 1 to N do     if 2 &^ Psis[k] mod n = r then A[n]:= k; break fi   od:   if not assigned(A[n]) then break fi od: seq(A[i], i=1..n-1); # Robert Israel, Aug 29 2017 MATHEMATICA psi[n_] := If[n == 1, 1, n Times @@ (1 + 1/First /@ FactorInteger@ n)]; a[n_] := Block[{k = 1, v = PowerMod[2, EulerPhi[n], n]}, While[ PowerMod[2, psi[k], n] != v, k++]; k]; Array[a, 83] (* Giovanni Resta, Aug 30 2017 *) 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 (Mod(2, n)^a001615(k) != 2^eulerphi(n), k++); k; } \\ after Charles R Greathouse IV at A001615 CROSSREFS Cf. A000010, A001615, A002326. Sequence in context: A165601 A324030 A275821 * A265157 A054263 A308656 Adjacent sequences:  A291671 A291672 A291673 * A291675 A291676 A291677 KEYWORD nonn AUTHOR Altug Alkan, Aug 29 2017 STATUS approved

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Last modified March 31 16:23 EDT 2020. Contains 333151 sequences. (Running on oeis4.)