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

Author

Ant King, Apr 20 2007

Keywords

• easy
• nonn

Examples

			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.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..750
• Eric Weisstein's World of Mathematics, Unitary Divisor.

Crossrefs

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

Programs

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

Formula

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