A121853 Cumulative product of A000120.

1, 1, 1, 2, 2, 4, 8, 24, 24, 48, 96, 288, 576, 1728, 5184, 20736, 20736, 41472, 82944, 248832, 497664, 1492992, 4478976, 17915904, 35831808, 107495424, 322486272, 1289945088, 3869835264, 15479341056, 61917364224, 309586821120, 309586821120, 619173642240

Offset

0,4

Comments

This sequence does not always have prime exponents decreasing (i.e., is not always a product of primorial numbers). The first exception is a(5932), which is divisible by 7^1214, but only by 5^1213.

Links

Amiram Eldar, Table of n, a(n) for n = 0..1000

Formula

a(n) = Product_{k=1..n} A000120(k).

Maple

a:= proc(n) option remember; `if`(n=0, 1,
      a(n-1)*add(i, i=Bits[Split](n)))
    end:
seq(a(n), n=0..40);  # Alois P. Heinz, Jul 29 2025

Mathematica

Join[{1}, FoldList[Times, Table[DigitCount[n, 2, 1], {n, 40}]]] (* Harvey P. Dale, Dec 08 2015 *)

Prog

(PARI) list(nmax) = {my(r = 1); print1(r, ", "); for(n = 1, nmax, r *= hammingweight(n); print1(r, ", ")); } \\ Amiram Eldar, Jul 29 2025

Crossrefs

Cf. A000120, A002110, A025487.

Sequence in context: A100396 A056630 A259813 * A064451 A223027 A325514

Adjacent sequences: A121850 A121851 A121852 * A121854 A121855 A121856

Keyword

nonn,base

Author

Franklin T. Adams-Watters, Aug 30 2006

Status

approved