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Position of highly composite numbers in the sequence of products of primorials.
8

%I #9 Mar 22 2019 00:31:53

%S 1,2,3,4,6,8,11,12,13,17,20,24,27,34,36,43,47,55,67,77,84,95,102,107,

%T 112,129,133,138,154,166,183,198,211,220,245,252,261,264,294,314,348,

%U 369,390,406,446,457,476,500,533,555,582,634,652,676,726,756,822

%N Position of highly composite numbers in the sequence of products of primorials.

%C Indices of A002182 in A025487. All terms in A002182 are products of terms in A002110; A025487 lists products of terms in A002110.

%C The first 28 terms of this sequence and those of A293635 are identical since the smallest 28 terms of A002182 and A004394 are the same.

%H Michael De Vlieger, <a href="/A306802/b306802.txt">Table of n, a(n) for n = 1..511</a>

%e The number 120 is 10th in the sequence of highly composite numbers, since it sets a record for the divisor counting function. The index of this number in A025487 is 17.

%t Block[{P = Product[Prime@ i, {i, 8}], s, t, u}, s = Array[DivisorSigma[0, #] &, P]; t = Array[If[# == 1, {0}, Sort[FactorInteger[#][[All, -1]], Greater]] &, P]; u = Values[PositionIndex@ t][[All, 1]]; Map[FirstPosition[u, #][[1]] &, FirstPosition[s, #][[1]] & /@ Union@ FoldList[Max, s]] ]

%Y Cf. A002182, A025487, A098719, A293635.

%K nonn

%O 1,2

%A _Michael De Vlieger_, Mar 12 2019