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Numbers n such that sigma(n+3) - sigma(n) = n + 3.
4

%I #20 Sep 08 2022 08:46:09

%S 7,6285,4693485,54028959,75898473,724416741,2359059709,4901493769,

%T 321212249593,511578306649,534245763769,6158645822473

%N Numbers n such that sigma(n+3) - sigma(n) = n + 3.

%C Also numbers n such that A001065(n+3) = A000203(n). - _Michel Marcus_, Sep 06 2014

%C a(13) > 10^13. - _Giovanni Resta_, Jul 13 2015

%e Number 7 is in sequence because sigma(7+3) - sigma(7) = 18 - 8 = 10 = 7 + 3.

%o (Magma) [n:n in[1..10^7] | SumOfDivisors(n+3)-SumOfDivisors(n) eq n+3]

%o (PARI)

%o for(n=1,10^7,if(sigma(n+3)-sigma(n)==n+3,print1(n,", "))) \\ _Derek Orr_, Sep 05 2014

%Y Cf. A000203, A067816, A246851, A246852, A246854, A246855.

%K nonn,more

%O 1,1

%A _Jaroslav Krizek_, Sep 05 2014

%E a(4)-a(8) from _Hiroaki Yamanouchi_, Sep 10 2014

%E a(9)-a(12) from _Giovanni Resta_, Jul 13 2015