A129499 - OEIS

%I #8 Jul 30 2019 07:49:39

%S 30,210,330,390,510,570,690,870,930,1110,1230,1290,1410,1470,1590,

%T 1770,1830,2010,2130,2190,2310,2730,3570,3990,4830,5610,6090,6510,

%U 7590,7770,8610,9030,9870,11130,12390,12810,14070,14910,15330,16590,17430,18690

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

%H Amiram Eldar, <a href="/A129499/b129499.txt">Table of n, a(n) for n = 1..750</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/UnitaryDivisor.html">Unitary Divisor</a>.

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

%e 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.

%t 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

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

%K easy,nonn

%O 1,1

%A _Ant King_, Apr 20 2007