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%I #11 Mar 11 2014 22:11:51
%S 434,305635357,27,39,106645,69,2275,63,6475,249,7735,3703,10803,16383,
%T 58869,51181,87951,1695,9579,105237,98829,1143369,789609,11625,
%U 14038691,178975,48627929,1881333,402373721,2667945,82915599,353195221,70106601
%N Smallest composite x such that sigma(x+2^n) = sigma(x) + 2^n.
%C The sequence is initiated by smallest of A015915. Special primes of A023202, A049488-A049491 also satisfy the Sigma[p+2^w]=Sigma[p]+2^w relation
%e For the term 69: Sigma[69+2^6] = Sigma[133] = 1+7+19+133 = Sigma[69]+64 = (1+3+23+69)+64 = 160.
%t Table[ Select[ Range[ 1, 110000 ], Equal[ EulerPhi[ #+2^k ]-EulerPhi[ # ]-2^k, 0 ] &&!PrimeQ[ # ]& ], {k, 1, 22} ]
%o (PARI) a(n)=my(N=2^n,x=3); while(isprime(x++) || sigma(x+N) != sigma(x)+N,); x \\ _Charles R Greathouse IV_, Mar 11 2014
%Y Cf. A049488-A049491, A001359, A054799, A015913, A015915, A023200, A023202, A054905.
%K nonn
%O 1,1
%A _Labos Elemer_, May 29 2000
%E More terms from _Labos Elemer_, Aug 14 2003
%E a(21) corrected and a(27)-a(33) from _Donovan Johnson_, Nov 30 2008
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