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A329525 a(n) is the smallest positive number k such that k and k+n are both abundant.

%I A329525 #16 Aug 28 2024 14:58:38
%S A329525 5775,18,942,20,940,12,945,12,936,20,4725,12,4712,40,930,20,928,12,
%T A329525 2816,20,924,18,945,12,920,30,918,12,2176,12,3465,24,912,20,910,12,
%U A329525 7208,18,906,20,4095,12,5312,12,900,20,945,12,896,20,894,18,4672,12,945,24
%N A329525 a(n) is the smallest positive number k such that k and k+n are both abundant.
%C A329525 Sequences of numbers k such that k and k+n are both abundant for any n: A096399 (n = 1), A231086 (n = 2).
%H A329525 Antti Karttunen, <a href="/A329525/b329525.txt">Table of n, a(n) for n = 1..20000</a>
%e A329525 Number 5775 is the smallest abundant number k such that k+1 = 5576 is also abundant.
%o A329525 (Magma) [Min([m: m in[1..10^4] | SumOfDivisors(m) gt 2*m and SumOfDivisors(m+n) gt 2*(m+n)]): n in [1..60]];
%o A329525 (PARI) A329525(n) = for(k=1, oo, if((sigma(k) > (k+k)) && (sigma(n+k) > 2*(n+k)), return(k))); \\ _Antti Karttunen_, Nov 15 2019
%Y A329525 Cf. A005101, A096399, A231086, A294937.
%K A329525 nonn
%O A329525 1,1
%A A329525 _Jaroslav Krizek_, Nov 15 2019