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Search: id:A055487
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| A055487 |
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Least m such that EulerPhi[m] = n!. |
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+0
4
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| 1, 3, 7, 35, 143, 779, 5183, 40723, 364087, 3632617, 39916801, 479045521, 6227180929, 87178882081, 1307676655073, 20922799053799, 355687465815361, 6402373865831809, 121645101106397521, 2432902011297772771
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Erdos believed (see Guy reference) that Phi[x] = n! is solvable.
Factorial primes of p = A002981[m]!+1 = k!+1 form give smallest solutions for some m [like m = 1,2,3,11] as follows: Phi[p] = p-1 = A002981[m]!.
According to Tattersall, in 1950 H. Gupta showed that phi(x) = n! is always solvable. - Joseph L. Pe (joseph_l_pe(AT)hotmail.com), Oct 01 2002
A123476(n) is a solution to the equation phi(x)=n! - T. D. Noe (noe(AT)sspectra.com), Sep 27 2006
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REFERENCES
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R. K. Guy, (1981): Unsolved problems In Number Theory, Springer - page 53.
Tattersall, J. "Elementary Number Theory in Nine Chapters", Cambridge University Press, 2001, p. 162.
P. Erdos and J. Lambek, Problem 4221, Amer. Math. Monthly, 55 (1948), 103.
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FORMULA
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a(n) = Min{m : Phi[m] = n!} = Min{m : A000010(m) = A000142(n)}
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CROSSREFS
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Cf. A055486-A055489, A055506, A000010, A000142.
Adjacent sequences: A055484 A055485 A055486 this_sequence A055488 A055489 A055490
Sequence in context: A024496 A081890 A047907 this_sequence A121130 A006099 A053530
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KEYWORD
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nonn
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AUTHOR
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Labos E. (labos(AT)ana.sote.hu), Jun 28 2000
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EXTENSIONS
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More terms from djr(AT)nk.ca, Nov 05 2001
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