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Numbers that can be expressed both as the sum of first deficient numbers and as the sum of first abundant numbers.
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%I #21 Feb 27 2018 06:19:52

%S 30,8388,10093090395,107318445076,123649798600,28404836330575,

%T 85678144827202815,456013868127570451

%N Numbers that can be expressed both as the sum of first deficient numbers and as the sum of first abundant numbers.

%C Intersection of A173106 and A173107.

%e The first seven deficient numbers sum to 1 + 2 + 3 + 4 + 5 + 7 + 8 = 30 and the first two abundant numbers sum to 12 + 18 = 30.

%e The sum of first 113 deficient numbers and the sum of first 61 abundant numbers are equal to 8388.

%p with(numtheory): P:=proc(q) local a,b,c,d,n; a:=0; b:=0; c:=0; d:=0;

%p for n from 1 to q do b:=b+1; while sigma(b)<=2*b do b:=b+1; od; a:=a+b;

%p while c<a do d:=d+1; if sigma(d)<2*d then c:=c+d; fi; od;

%p if c=a then print(a); fi; od; end: P(10^9);

%Y Cf. A005100, A005101, A173106, A173107.

%K nonn,more

%O 1,1

%A _Paolo P. Lava_, Feb 26 2018

%E a(6)-a(8) from _Giovanni Resta_, Feb 26 2018