

A234899


Record holders for lengths of everdecreasing aliquot sequences.


2



1, 2, 4, 9, 14, 16, 26, 46, 52, 166, 212, 1113, 2343, 4437, 5145, 8535, 10665, 18711, 33682, 64935, 114808, 187232, 228316, 304412, 464132, 556636, 623288, 1230284, 1319956, 1508504, 2897884, 3835556, 7487494, 9446906, 16871648, 22328212, 29668150, 29725184
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OFFSET

1,2


COMMENTS

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.
The current sequence lists the deficient numbers yielding uninterrupted decreasing aliquot sequences that are longer than any previous ones (compare with A081699).
Note that, so far, the lengths of the corresponding sequences are contiguous. Does it remain so for next terms?


LINKS



EXAMPLE

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.


PROG

(PARI) nbdecr(n) = {nb = 0; while (n && ((newn = sigma(n)n)) < n, n = newn ; nb++); nb; }
lista(nn) = {recab = 0; for (ni = 1, nn, ab = nbdecr(ni); if (ab > recab, recab = ab; print1(ni, ", ")); ); }


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



