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Indices of records in A299990.
4

%I #8 Mar 03 2018 14:58:25

%S 1,30,42,66,78,90,102,114,138,150,210,330,390,510,570,630,870,990,

%T 1050,1470,1890,2100,2310,2730,3570,3990,4620,5460,6510,6930,8190,

%U 9240,10710,11550,13650,16170,19110,20790,23100,24570,25410,30030,39270,43890,46410

%N Indices of records in A299990.

%C A010846(n) = A000005(n) + A243822(n).

%C Successive terms in this sequence represent increasing differences A243822(n) - A000005(n).

%C A000079 = records in -1 * A299990, since A243822(p^e)=0 for e>=0, n = 2^k sets records in A000005(n). The corresponding records are in A000027.

%H Michael De Vlieger, <a href="/A300156/b300156.txt">Table of n, a(n) for n = 1..108</a>

%H Michael De Vlieger, <a href="/A300156/a300156.txt">Relationships between A244052, A294492, and A300156</a>.

%e The first term is 1: A299990(1) = -1. The first term that exceeds -1 in A299990 corresponds to n = 30; A299990(30) = 2, thus 30 is the second term.

%t With[{s = Table[Count[Range[n], _?(PowerMod[n, Floor@ Log2@ n, #] == 0 &)] - 2 DivisorSigma[0, n], {n, 10^3}]}, Map[FirstPosition[s, #][[1]] &, Union@ FoldList[Max, s]]]

%Y Cf. A000005, A000027, A000079, A010846, A243822, A299990, A299991, A299992, A300155, A300157.

%K nonn

%O 1,2

%A _Michael De Vlieger_, Feb 26 2018