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A337776 a(n) is the order of A337775(n) (as defined in that sequence). 2
0, 1, 2, 2, 3, 3, 4, 2, 4, 4, 4, 3, 5, 3, 5, 5, 5, 5, 5, 5, 4, 4, 6, 6, 6, 4, 6, 6, 3, 6, 3, 6, 7, 6, 5, 4, 5, 4, 7, 5, 7, 5, 5, 7, 4, 5, 5, 4, 7, 4, 7, 7, 7, 3, 8, 7, 7, 4, 7, 7, 7, 6, 6, 5, 6, 6, 5, 6, 6, 6, 8, 8, 6, 6, 4, 6, 8, 6, 6, 8, 6, 6, 6, 5, 5, 8, 8, 5, 6, 6, 8, 8, 5, 5, 8, 4, 5 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,3
REFERENCES
J.-M. De Koninck, Ces nombres qui nous fascinent, Entry 108, p. 38, Ellipses, Paris 2008.
J.-M. De Koninck & A. Mercier, 1001 Problèmes en Théorie Classique Des Nombres, Problème 745 ; pp 95; 317-8, Ellipses Paris 2004.
LINKS
J.-M. De Koninck, When the Totient Is the Product of the Squared Prime Divisors: Problem 10966, Amer. Math. Monthly, 111 (2004), p. 536.
FORMULA
rad(A337775(n))^a(n) = phi(A337775(n)).
a(n) = log(phi(A337775(n))) / log(rad(A337775(n))). - Andrew Howroyd, Sep 21 2020
MATHEMATICA
nn = 97;
Sar = Table[0, {nn}]; Sar[[1]] = 2;
(*It is a list oh the sequence A337775*)
OrdSar = Table[0, {nn}]; OrdSar[[1]] = 0;
(*It is a sequence A337776 - the orders of members in sequence A337775*) For[Index = 2, Index <= nn, Index++,
InitialPrime = Prime[Index];
InitialInteger = InitialPrime - 1;
InitialArray = FactorInteger[InitialInteger];
For[i = 1, i <= Length[InitialArray], i++,
CurrentArray =
FactorInteger[InitialArray[[-i, 1]] - 1] ~Join~ InitialArray;
InitialInterger =
Product[CurrentArray[[k, 1]] ^ CurrentArray[[k, 2]], {k, 1,
Length[CurrentArray]}];
InitialArray = FactorInteger[InitialInterger];
];
InitialArray = InitialArray ~Join~ {{InitialPrime, 0}};
Ord = Max[InitialArray[[All, 2]]];
Lint = Product[
Power[InitialArray[[k, 1]], Ord - InitialArray[[k, 2]] + 1], {k,
1, Length[InitialArray]}];
radn = Product[InitialArray[[k, 1]], {k, 1, Length[InitialArray]}];
Sar[[Index]] = Lint;
OrdSar[[Index]] = Ord;
];
Print["Sar= ", Sar]
Print["OrdSar= ", OrdSar]
CROSSREFS
Cf. A000010 (phi), A000040 (prime), A007947 (rad), A337775.
Sequence in context: A339811 A015135 A116619 * A366611 A091220 A057955
KEYWORD
nonn
AUTHOR
Vladislav Shubin, Sep 20 2020
STATUS
approved

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Last modified March 29 06:34 EDT 2024. Contains 371265 sequences. (Running on oeis4.)