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A097652 Numbers n such that n=phi(phi(n)+sigma(n)) and n is not of the form 2*p where p is a Sophie Germain odd prime. 1
1, 2, 20, 48, 180, 208, 864, 1120, 1368, 3552, 58320, 76416, 79968, 95488, 107520, 338688, 570240, 595968, 653184, 1347840, 5199552, 7918848, 14592000, 93699072, 159138176, 167078784, 246688000, 281640960, 314548224, 323985408, 338411520, 347578368, 352002048 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

It is obvious that if n=2*p where p is a Sophie Germain odd prime then n=phi(phi(n)+sigma(n)). This sequence is a subsequence of A097646. Except for the first term all terms of this sequence are even. There is no other term up t0 3*10^7.

LINKS

Table of n, a(n) for n=1..33.

C. K. Caldwell, The Prime Glossary, Sophie Germain prime.

EXAMPLE

14592000 is in the sequence because 14592000=2*7296000, 7296000 is not a Sophie Germain odd prime and phi(phi(14592000)+sigma(14592000)) =14592000.

MATHEMATICA

Do[If[(!PrimeQ[n/2]||!PrimeQ[n+1])&&n==EulerPhi[EulerPhi[n]+ DivisorSigma[1, n]], Print[n]], {n, 30000000}]

CROSSREFS

Cf. A097646, A005384.

Sequence in context: A266842 A254542 A202602 * A261838 A225065 A059211

Adjacent sequences:  A097649 A097650 A097651 * A097653 A097654 A097655

KEYWORD

nonn

AUTHOR

Farideh Firoozbakht, Sep 09 2004

EXTENSIONS

a(24)-a(33) from Donovan Johnson, Jan 18 2012

STATUS

approved

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Last modified December 15 20:00 EST 2019. Contains 330000 sequences. (Running on oeis4.)