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

Author

Antti Karttunen, Dec 22 2019

Keywords

• nonn

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)

Crossrefs

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

Subsequence of A181815.

Programs

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 *)

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).

Extensions

More linking formulas added by Antti Karttunen, Jan 13 2020