A300157 Records in A299990.

-1, 2, 3, 6, 7, 8, 9, 10, 11, 17, 36, 45, 48, 54, 56, 67, 69, 76, 97, 118, 119, 120, 219, 231, 249, 258, 286, 299, 302, 356, 367, 377, 392, 455, 471, 533, 547, 563, 573, 576, 647, 1033, 1096, 1125, 1129, 1157, 1178, 1334, 1405, 1439, 1587, 1664, 1721, 1952

Offset: 1

Author

Michael De Vlieger, Feb 26 2018

Keywords

• sign

Comments

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

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.

Number of terms less than 10^k with 0 <= k <= 7: {0, 1, 6, 18, 32, 51, 68, 96}.

Examples

			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.
		

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..108

Crossrefs

Cf. A000005, A000027, A000079, A010846, A243822, A299990, A299991, A299992, A300155, A300156.

Programs

Mathematica

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