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A062402 Sigma(phi(n)). +0
42
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)
OFFSET

1,3

COMMENT

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

REFERENCES

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.

LINKS

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).

FORMULA

sigma[A062401(x)]=a(sigma[x]) or phi[a(x)]=A062401(phi[x]). - Labos E. (labos(AT)ana.sote.hu), Jul 22 2004

EXAMPLE

a(9)= 12 because phi(9)= 6 and sigma(6)= 12.

PROGRAM

(PARI) j(e)=sigma(eulerphi(n)); vector(150, n, j(e))

CROSSREFS

Cf. A000203, A000010, A062401.

Cf. A096852, A096857, A096994, A096995.

Sequence in context: A083262 A122978 A119347 this_sequence A156838 A100587 A099282

Adjacent sequences: A062399 A062400 A062401 this_sequence A062403 A062404 A062405

KEYWORD

nonn

AUTHOR

Jason Earls (zevi_35711(AT)yahoo.com), Jul 08 2001

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Last modified November 24 23:16 EST 2009. Contains 167481 sequences.


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