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 A270562 a(n) is the largest number m satisfying lambda(m)=n, or zero if there is no solution, where lambda(m) is Carmichael's lambda function A002322(m). 4
 2, 24, 0, 240, 0, 504, 0, 480, 0, 264, 0, 65520, 0, 0, 0, 16320, 0, 28728, 0, 13200, 0, 552, 0, 131040, 0, 0, 0, 6960, 0, 171864, 0, 32640, 0, 0, 0, 138181680, 0, 0, 0, 1082400, 0, 151704, 0, 5520, 0, 1128, 0, 4455360, 0, 0, 0, 12720, 0, 86184, 0, 13920, 0, 1416, 0, 6814407600, 0, 0, 0, 65280 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS a(n) is the largest modulus m such that the largest order of any element in the multiplicative group modulo m is n; a(n) is zero if there is no such group with largest order n. Omitting the zeros gives A143407. a(n) = 0 if n is not a term of A002174. LINKS Gheorghe Coserea, Table of n, a(n) for n = 1..50005 R. D. Carmichael, Note on a new number theory function, Bull. Amer. Math. Soc. 16 (1910), 232-238. MATHEMATICA a[n_] := Module[{f, fsz, g = 1, h = 1, p, e}, Which[n <= 0, Return[0], n == 1, Return[2], OddQ[n], Return[0]]; f = FactorInteger[n][[All, 1]]; fsz = Length[f]; For[k = 1, k <= fsz, k++, p = f[[k]]; e = 1; While[Mod[n, CarmichaelLambda[p^e]] == 0, e++]; g *= p^(e-1)]; Do[If[PrimeQ[d+1] && Mod[g, d+1] != 0, h *= (d+1)], {d, Divisors[n]}]; g *= h; If[CarmichaelLambda[g] != n, 0, g]]; a /@ Range[100] (* Jean-François Alcover, Oct 18 2019, after Gheorghe Coserea *) PROG (PARI, from Gheorghe Coserea, Feb 21 2019) lambda(n) = { \\ A002322 my(f=factor(n), fsz=matsize(f)[1]); lcm(vector(fsz, k, my(p=f[k, 1], e=f[k, 2]); if (p != 2, p^(e-1)*(p-1), e > 2, 2^(e-2), 2^(e-1)))); }; a(n) = { if (n <= 0, return(0), n==1, return(2), n%2, return(0)); my(f=factor(n), fsz=matsize(f)[1], g=1, h=1); for (k=1, fsz, my(p=f[k, 1], e=1); while (n % lambda(p^e) == 0, e++); g *= p^(e-1)); fordiv(n, d, if (isprime(d+1) && g % (d+1) != 0, h *= (d+1))); g *= h; if (lambda(g) != n, 0, g); }; vector(64, n, a(n)) CROSSREFS Cf. A002322, A002174, A051222, A143407, A270564, A111725. See also A321713 (number of solutions). Sequence in context: A228241 A054909 A171636 * A100816 A079612 A329263 Adjacent sequences:  A270559 A270560 A270561 * A270563 A270564 A270565 KEYWORD nonn AUTHOR Joerg Arndt, Mar 19 2016 EXTENSIONS Corrected and extended by Gheorghe Coserea, Feb 21 2019 Entry revised by N. J. A. Sloane, May 03 2019 STATUS approved

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Last modified January 15 10:12 EST 2021. Contains 340187 sequences. (Running on oeis4.)