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A234899 Record holders for lengths of ever-decreasing aliquot sequences. 1

%I

%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?

%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

%O 1,2

%A _Michel Marcus_, Jan 01 2014

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Last modified May 24 05:06 EDT 2022. Contains 354005 sequences. (Running on oeis4.)