A284001 a(n) = A005361(A283477(n)).

1, 1, 1, 2, 1, 2, 4, 6, 1, 2, 4, 6, 8, 12, 18, 24, 1, 2, 4, 6, 8, 12, 18, 24, 16, 24, 36, 48, 54, 72, 96, 120, 1, 2, 4, 6, 8, 12, 18, 24, 16, 24, 36, 48, 54, 72, 96, 120, 32, 48, 72, 96, 108, 144, 192, 240, 162, 216, 288, 360, 384, 480, 600, 720, 1, 2, 4, 6, 8, 12, 18, 24, 16, 24, 36, 48, 54, 72, 96, 120, 32, 48, 72, 96, 108, 144, 192, 240, 162, 216, 288, 360, 384, 480

Offset

0,4

Comments

a(n) is the product of elements of the multiset that covers an initial interval of positive integers with multiplicities equal to the parts of the n-th composition in standard order (graded reverse-lexicographic, A066099). This composition is obtained by taking the set of positions of 1's in the reversed binary expansion of n, prepending 0, taking first differences, and reversing again. For example, the 13th composition is (1,2,1) giving the multiset {1,2,2,3} with product 12, so a(13) = 12. - Gus Wiseman, Apr 26 2020

Links

Antti Karttunen, Table of n, a(n) for n = 0..8191

Index entries for sequences related to binary expansion of n

Formula

a(n) = A005361(A283477(n)).

a(n) = A003963(A057335(n)). - Gus Wiseman, Apr 26 2020

a(n) = A284005(A053645(n)) for n > 0 with a(0) = 1. - Mikhail Kurkov, Jun 05 2021 [verification needed]

Mathematica

Table[Times @@ FactorInteger[#][[All, -1]] &[Times @@ Map[#1^#2 & @@ # &, FactorInteger[#] /. {p_, e_} /; e == 1 :> {Times @@ Prime@ Range@ PrimePi@ p, e}] &[Times @@ Prime@ Flatten@ Position[#, 1] &@ Reverse@ IntegerDigits[n, 2]]], {n, 0, 93}] (* Michael De Vlieger, Mar 18 2017 *)

Prog

(PARI)
A005361(n) = factorback(factor(n)[, 2]); \\ From A005361
A034386(n) = prod(i=1, primepi(n), prime(i));
A108951(n) = { my(f=factor(n)); prod(i=1, #f~, A034386(f[i, 1])^f[i, 2]) };  \\ From A108951
A019565(n) = {my(j, v); factorback(Mat(vector(if(n, #n=vecextract(binary(n), "-1..1")), j, [prime(j), n[j]])~))}; \\ From A019565
A283477(n) = A108951(A019565(n));
A284001(n) = A005361(A283477(n));
(Scheme) (define (A284001 n) (A005361 (A283477 n)))

Crossrefs

Cf. A005361, A283477, A284002, A284005.

Row products of A095684.

All of the following pertain to compositions in standard order (A066099):

- Length is A000120.

- Weighted sum is A029931.

- Necklaces are A065609.

- Sum is A070939.

- Strict compositions are A233564.

- Constant compositions are A272919.

- Lyndon words are A275692.

- Distinct parts are counted by A334028.

Cf. A003963, A034691, A053645, A057335, A305936, A318284, A333764, A333940, A333942, A334030.

Sequence in context: A138256 A214783 A360279 * A139145 A201635 A179787

Adjacent sequences: A283998 A283999 A284000 * A284002 A284003 A284004

Keyword

nonn,look

Author

Antti Karttunen, Mar 18 2017

Status

approved