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Search: id:A062402
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| 1, 1, 3, 3, 7, 3, 12, 7, 12, 7, 18, 7, 28, 12, 15, 15, 31, 12, 39, 15, 28, 18, 36, 15, 42, 28, 39, 28, 56, 15, 72, 31, 42, 31, 60, 28, 91, 39, 60, 31, 90, 28, 96, 42, 60, 36, 72, 31, 96, 42, 63, 60, 98, 39, 90, 60, 91, 56, 90, 31, 168, 72, 91, 63, 124, 42, 144, 63, 84, 60, 144
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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Makowski and Schinzel conjectured in 1964 that a(n)=sigma(phi(n))>=n/2 for all n (B42 of Guy Unsolved Problems...). This has been verified for various classes of numbers and proved to be true in general if it is true for squarefree integers (see Cohen's paper). - Antonio G. Astudillo (afg_astudillo(AT)hotmail.com), Sep 07 2002
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REFERENCES
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A. Grytczuk, F. Luca and M. Wojtowicz, On a conjecture of Makowski and Schinzel concerning the composition of the arithmetic functions $\sigma$ and $\phi$. Colloq. Math. 86, No. 1, 31-36 (2000).
F. Luca and C. Pomerance, On some problems of Makowski-Schinzel and Erdos concerning the arithmetical functions $\phi$ and $\sigma$. Colloq. Math. 92, No. 1, 111-130 (2002).
A. Makowski and A. Schinzel, On the functions phi(n) and sigma(n), Colloq. Math. 13, 95-99 (1964).
D. S. Mitrinovic et al., Handbook of Number Theory, Kluwer, p. 13.
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..10000
G. L. Cohen, On a conjecture of Makowski and Schinzel. Colloq. Math. 74, No. 1, 1-8 (1997).
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FORMULA
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sigma[A062401(x)]=a(sigma[x]) or phi[a(x)]=A062401(phi[x]). - Labos E. (labos(AT)ana.sote.hu), Jul 22 2004
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EXAMPLE
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a(9)= 12 because phi(9)= 6 and sigma(6)= 12.
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PROGRAM
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(PARI) j(e)=sigma(eulerphi(n)); vector(150, n, j(e))
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CROSSREFS
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Cf. A000203, A000010, A062401.
Cf. A096852, A096857, A096994, A096995.
Sequence in context: A083262 A122978 A119347 this_sequence A100587 A099282 A002937
Adjacent sequences: A062399 A062400 A062401 this_sequence A062403 A062404 A062405
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KEYWORD
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nonn
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AUTHOR
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Jason Earls (zevi_35711(AT)yahoo.com), Jul 08 2001
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