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%I #12 Apr 11 2024 04:11:18
%S 1,2,4,9,14,16,26,46,52,166,212,1113,2343,4437,5145,8535,10665,18711,
%T 33682,64935,114808,187232,228316,304412,464132,556636,623288,1230284,
%U 1319956,1508504,2897884,3835556,7487494,9446906,16871648,22328212,29668150,29725184
%N Record holders for lengths of ever-decreasing aliquot sequences.
%C If one looks at the lengths of uninterrupted decreasing aliquot sequences, the converse of A081705, one gets a sequence similar to A098008, except for perfect or abundant numbers, but also for numbers that encounter a perfect or abundant numbers in this process.
%C The current sequence lists the deficient numbers yielding uninterrupted decreasing aliquot sequences that are longer than any previous ones (compare with A081699).
%C Note that, so far, the lengths of the corresponding sequences are contiguous. Does it remain so for next terms?
%H Amiram Eldar, <a href="/A234899/b234899.txt">Table of n, a(n) for n = 1..59</a>
%e The aliquot sequence starting at 2 decreases as follows 2->1->0 and is longer than the sequence starting at 1. Hence 2 is in the sequence.
%o (PARI) nbdecr(n) = {nb = 0; while (n && ((newn = sigma(n)-n)) < n, n = newn ; nb++); nb;}
%o lista(nn) = {recab = 0; for (ni = 1, nn, ab = nbdecr(ni); if (ab > recab, recab = ab; print1(ni, ", ")););}
%Y Cf. A081699, A081705, A098008.
%K nonn,changed
%O 1,2
%A _Michel Marcus_, Jan 01 2014
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