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

1,2

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.

Links

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

Example

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.

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]] ]

Crossrefs

Cf. A002182, A025487, A098719, A293635.

Sequence in context: A182417 A189704 A223543 * A293635 A123586 A257121

Adjacent sequences: A306799 A306800 A306801 * A306803 A306804 A306805

Keyword

nonn

Author

Michael De Vlieger, Mar 12 2019

Status

approved