A074329 The n-th highly composite number equals the a(n)-th composite number, for n >= 3.

0, 0, 1, 2, 6, 14, 24, 32, 42, 89, 138, 187, 287, 591, 693, 1054, 1416, 2151, 4364, 6600, 8842, 13354, 17879, 22418, 24697, 40653, 45227, 49811, 75040, 100357, 151121, 202000, 252981, 304025, 457506, 508744, 611307, 662636, 996722, 1331409

Offset

1,4

Comments

Since the first 2 highly composite numbers, 1 and 2, are not composite numbers, the first 2 terms here were taken to be 0.

Links

Amiram Eldar, Table of n, a(n) for n = 1..217

Formula

a(n) = A002182(n) - A000720(A002182(n)) - 1.

A002808(a(n)) = A002182(n).

Example

The 6th highly composite number is 24, the 14th composite number, so a(6) = 14.

Mathematica

t[x_] := A002182[x]; Table[Part[t, w]-PrimePi[Part[t, w]]-1, {w, 1, Length[t]}]

Crossrefs

Cf. A002182, A002808, A000720.

Sequence in context: A307643 A239877 A032386 * A109592 A238410 A256482

Adjacent sequences: A074326 A074327 A074328 * A074330 A074331 A074332

Keyword

nonn

Author

Labos Elemer, Aug 21 2002

Status

approved