A036493 -id:A036493 - cp's OEIS frontend

A036470 a(n) is the number of distinct possible values of d(k), the number of divisors of k, among numbers k whose binary order (A029837) does not exceed n.

1, 2, 3, 4, 6, 7, 11, 12, 16, 17, 23, 26, 31, 37, 43, 48, 58, 64, 74, 82, 94, 106, 122, 133, 146, 165, 183, 202, 224, 244, 267, 294, 325, 355, 389, 416, 453, 500, 541, 584, 636, 680, 737, 795, 859, 922, 995, 1068, 1149, 1233, 1324, 1412, 1523, 1616, 1731, 1845

Offset: 0

Labos Elemer

nonn

			If 1 <= k <= 128, i.e., the binary order of k is g(k) <= 7, then d(k) takes 12 values {1,2,3,4,5,6,7,8,9,10,12,16}; thus a(7) = 12. The maximal value (16) appears as a(7) in A036451.

David A. Corneth, Table of n, a(n) for n = 0..63

Cf. A000005, A005179, A029837, A036471, A036493.

a(20)-a(21) corrected by David A. Corneth, May 12 2018

A036484 a(n) is the minimal number of binary order n which has maximal number of divisors in this interval.

Original entry on oeis.org

1, 2, 4, 6, 12, 24, 60, 120, 240, 360, 840, 1680, 2520, 7560, 15120, 27720, 55440, 110880, 221760, 498960, 720720, 1441440, 3603600, 7207200, 14414400, 32432400, 61261200, 122522400, 245044800, 367567200, 735134400, 2095133040

Offset: 0

Labos Elemer

Compare with A007416, where terms of this sequence are present.

			For n=9, with 256 < k <= 512, d(k) takes 17 distinct values, of which d(k)=24 is the greatest (see A036451 and A036470) and occurs first at k=360, so a(9)=360.

Cf. A000005, A029837, A005179, A007416, A036470, A036492, A036493.

Block[{nn = 22, s}, s = TakeList[Array[DivisorSigma[0, # + 1] &, 2^nn - 1], 2^Range[0, nn - 1]]; {1}~Join~Map[2^(#1 - 1) + #2 & @@ FirstPosition[s, #] &, Map[Max, s]]] (* Michael De Vlieger, Nov 04 2020 *)

a(22)-a(31) from Sean A. Irvine, Nov 04 2020

cp's OEIS Frontend

A036470 a(n) is the number of distinct possible values of d(k), the number of divisors of k, among numbers k whose binary order (A029837) does not exceed n.

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