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

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

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

Amiram Eldar, Table of n, a(n) for n = 1..59

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

Cf. A081699, A081705, A098008.

Sequence in context: A085901 A077224 A059447 * A190553 A270532 A281407

Adjacent sequences: A234896 A234897 A234898 * A234900 A234901 A234902

Keyword

nonn

Author

Michel Marcus, Jan 01 2014

Status

approved