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%I #7 Mar 03 2018 14:58:36
%S -1,2,3,6,7,8,9,10,11,17,36,45,48,54,56,67,69,76,97,118,119,120,219,
%T 231,249,258,286,299,302,356,367,377,392,455,471,533,547,563,573,576,
%U 647,1033,1096,1125,1129,1157,1178,1334,1405,1439,1587,1664,1721,1952
%N Records in A299990.
%C A010846(n) = A000005(n) + A243822(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.
%C Number of terms less than 10^k with 0 <= k <= 7: {0, 1, 6, 18, 32, 51, 68, 96}.
%H Michael De Vlieger, <a href="/A300157/b300157.txt">Table of n, a(n) for n = 1..108</a>
%e A299990(1) = -1, thus this is the first record. A299990(30) = 2 and is the first term greater than -1, thus 30 is the second term of this sequence. Observe that A243822(1) is 0 and A000005(1) is 1; 0 - 1 = -1. A243822(30) is 10 and A000005(30) = 8; 10 - 8 = 2.
%t Union@ FoldList[Max, Table[Count[Range[n], _?(PowerMod[n, Floor@ Log2@ n, #] == 0 &)] - 2 DivisorSigma[0, n], {n, 10^3}]]
%Y Cf. A000005, A000027, A000079, A010846, A243822, A299990, A299991, A299992, A300155, A300156.
%K sign
%O 1,2
%A _Michael De Vlieger_, Feb 26 2018
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