A129499 Records for unitary abundant numbers, i.e., those integers which set a record for having a greater unitary abundance than any of their predecessors.

30, 210, 330, 390, 510, 570, 690, 870, 930, 1110, 1230, 1290, 1410, 1470, 1590, 1770, 1830, 2010, 2130, 2190, 2310, 2730, 3570, 3990, 4830, 5610, 6090, 6510, 7590, 7770, 8610, 9030, 9870, 11130, 12390, 12810, 14070, 14910, 15330, 16590, 17430, 18690

Offset

1,1

Links

Amiram Eldar, Table of n, a(n) for n = 1..750

Eric Weisstein's World of Mathematics, Unitary Divisor.

Formula

Values of A034683 corresponding to those positions in A129498 at which records occur.

Example

A129498 begins 12, 12, 12, 4, 12, 12, 12, 12, 12, 12, 12, 156, 12, 12. The second record value is 156, which occurs at position 12. As A034683(12)=210, it follows that a(2)=210.

Mathematica

UnitaryDivisors[n_Integer?Positive]:=Select[Divisors[n], GCD[ #, n/# ]==1&]; sstar[n_]:=Plus@@UnitaryDivisors[n]-n; RunningMaxima[l_]:=Rest[FoldList[Max, -Infinity, l]] HighWaterMarks[l_]:=Module[{s=Split[RunningMaxima[l]]}, {First/@s, Most[FoldList[Plus, 1, Length/@s]]} ]; data1=Select[Range[20000], sstar[ # ]-#>0 &]; data2=sstar[ # ]-# &/@data1; pos=Last[HighWaterMarks[data2]]; champs=data1[[ # ]] &/@pos

Crossrefs

Cf. A034448, A034460, A034683, A129468, A129498.

Sequence in context: A203617 A181629 A346245 * A286763 A347828 A069965

Adjacent sequences: A129496 A129497 A129498 * A129500 A129501 A129502

Keyword

easy,nonn

Author

Ant King, Apr 20 2007

Status

approved