A329902 Primorial deflation of the n-th highly composite number: the unique integer k such that A108951(k) = A002182(n).

1, 2, 4, 3, 6, 12, 9, 24, 10, 20, 15, 40, 30, 60, 28, 21, 56, 42, 84, 63, 168, 126, 336, 140, 66, 189, 280, 132, 99, 264, 198, 528, 220, 396, 297, 440, 792, 156, 117, 312, 234, 624, 260, 468, 351, 520, 936, 390, 1040, 1872, 780, 585, 306, 1560, 340, 612, 459, 680, 1224, 510, 1360, 2448, 1020, 765, 342, 2040, 1530, 684, 513

Offset

1,2

Links

Antti Karttunen, Table of n, a(n) for n = 1..10000 (computed from the b-file of A002182)

Michael De Vlieger, List of a(n) for n = 1..779674 (gzipped text file, prepared from Flammenkamp's data)

Michael De Vlieger, List of a(n) for n = 1..500000 (noncompressed text file, an abridged version of above)

Formula

a(n) = A329900(A002182(n)) = A319626(A002182(n)).

a(n) = A181815(A306802(n)).

A108951(a(n)) = A002182(n). [Highly composite numbers (undeflated)]

A056239(a(n)) = A112778(n). [Number of prime factors, counted with multiplicity]

A001222(a(n)) = A112779(n). [Largest exponent in the prime factorization]

A329605(a(n)) = A002183(n). [Number of divisors]

A329040(a(n)) = A324381(n).

A324888(a(n)) = A324382(n).

a(A330748(n)) = A330743(n).

Mathematica

Map[Times @@ Prime@(TakeWhile[Reap[FixedPointList[Block[{k = 1}, While[Mod[#, Prime@ k] == 0, k++]; Sow[k - 1]; #/Product[Prime@ i, {i, k - 1}]] &, #]][[-1, 1]], # > 0 &]) &, Take[Import["https://oeis.org/b002182.txt", "Data"][[All, -1]], 69] ] (* Michael De Vlieger, Jan 13 2020, imports b-file at A002182 *)

Crossrefs

Cf. A002182, A002183, A056239, A108951, A112778, A112779, A306802, A319626, A324381, A324382, A324581, A324582, A324888, A329040, A329605, A329900, A330743, A330748.

Subsequence of A181815.

Sequence in context: A046793 A182940 A101278 * A366028 A091274 A330745

Adjacent sequences: A329899 A329900 A329901 * A329903 A329904 A329905

Keyword

nonn

Author

Antti Karttunen, Dec 22 2019

Extensions

More linking formulas added by Antti Karttunen, Jan 13 2020

Status

approved