A306802 Position of highly composite numbers in the sequence of products of primorials.

1, 2, 3, 4, 6, 8, 11, 12, 13, 17, 20, 24, 27, 34, 36, 43, 47, 55, 67, 77, 84, 95, 102, 107, 112, 129, 133, 138, 154, 166, 183, 198, 211, 220, 245, 252, 261, 264, 294, 314, 348, 369, 390, 406, 446, 457, 476, 500, 533, 555, 582, 634, 652, 676, 726, 756, 822

Offset: 1

Author

Michael De Vlieger, Mar 12 2019

Keywords

• nonn

Comments

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

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.

Examples

			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.
		

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..511

Crossrefs

Cf. A002182, A025487, A098719, A293635.

Programs

Mathematica

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]] ]