cp's OEIS Frontend

A254879 Let us denote 's' the sum of the deficient numbers in the aliquot parts of x. Sequence lists numbers x such that sigma(s)-s is equal to x.

%I A254879 #16 Feb 19 2015 08:40:22
%S A254879 6,28,54,284,496,1184,1210,2924,5564,6232,6368,8128,10744,10856,14595,
%T A254879 18150,18416,66928,66992,71145,76084,87633,88730,123152,124155,139815,
%U A254879 153176,168730,176336,180848,193720,202444,203432,365084,389924,399592,430402,455344
%N A254879 Let us denote 's' the sum of the deficient numbers in the aliquot parts of x. Sequence lists numbers x such that sigma(s)-s is equal to x.
%C A254879 Perfect numbers belong to the sequence.
%H A254879 Paolo P. Lava, <a href="/A254879/b254879.txt">Table of n, a(n) for n = 1..100</a>
%e A254879 Aliquot parts of 28 are 1, 2, 4, 7, 14 and they are all deficient numbers: sigma(1 + 2 + 4 + 7 + 14) = sigma(28) = 56 and 56 - 28 = 28.
%e A254879 Aliquot parts of 18150 are 1, 2, 3, 5, 6, 10, 11, 15, 22, 25, 30, 33, 50, 55, 66, 75, 110, 121, 150, 165, 242, 275, 330, 363, 550, 605, 726, 825, 1210, 1650, 1815, 3025, 3630, 6050, 9075 and the deficient numbers are 1, 2, 3, 5,10, 11, 15, 22, 25, 33, 50, 55, 75, 110, 121, 165, 242, 275, 363, 605, 825, 1210, 1815, 3025, 9075:  sigma(1 + 2 + 3 + 5 + 10 + 11 + 15 + 22 + 25 + 33 + 50 + 55 + 75 + 110 + 121 + 165 + 242 + 275 + 363 + 605 + 825 + 1210 + 1815 + 3025 + 9075) = 18138 and sigma(18138) - 18138 = 18150.
%p A254879 with(numtheory); P:=proc(q) local a,b,k,n;
%p A254879 for n from 1 to q do a:=sort([op(divisors(n))]); b:=0;
%p A254879 for k from 1 to nops(a)-1 do if sigma(a[k])<2*a[k] then b:=b+a[k]; fi; od;
%p A254879 if sigma(b)-b=n then print(n); fi; od; end: P(10^9);
%Y A254879 Cf. A000396, A001065, A005100, A254878, A254880.
%K A254879 nonn
%O A254879 1,1
%A A254879 _Paolo P. Lava_, Feb 10 2015