A289272 Inverse to A289271.

1, 2, 3, 6, 4, 10, 12, 30, 5, 14, 15, 42, 20, 70, 60, 210, 7, 18, 21, 66, 28, 90, 84, 330, 35, 126, 105, 462, 140, 630, 420, 2310, 8, 22, 24, 78, 36, 110, 132, 390, 40, 154, 120, 546, 180, 770, 660, 2730, 56, 198, 168, 858, 252, 990, 924, 4290, 280, 1386, 840

Offset: 0

Author

Rémy Sigrist, Jun 30 2017

Keywords

• nonn
• base
• look

Comments

a(2^n-1) = A002110(n) for any n >= 0.

a(2^(n-1)) = A000961(n+1) for any n > 0.

A001221(a(n)) = A000120(n) for any n >= 0.

From Antti Karttunen, Jan 01 2019: (Start)

A034684(a(n)) = A000961(1+A001511(n)) for any n >= 1. (See also Rémy Sigrist's comment in A289271).

This sequence can be regarded also as an irregular triangle with rows of lengths 1, 1, 2, 4, 8, 16, ..., that is, it can be represented as a binary tree, where each left hand child contains A322991(k), and each right hand child contains A322992(k), when their parent contains k:

1

|

...................2...................

3 6

4......../ \........10 12......../ \........30

/ \ / \ / \ / \

/ \ / \ / \ / \

/ \ / \ / \ / \

5 14 15 42 20 70 60 210

7 18 21 66 28 90 84 330 35 126 105 462 140 630 420 2310

etc.

The leftmost edge is A000961, the next lefmost is A278568 (after 2: 6, 10, 14, 18, ...), the righmost edge is A002110, the next rightmost A088860 but with 3 instead of 4.

Compare also to trees like A005940 (A163511) and A052330.

(End)

Examples

			A289271(1) = 0, hence a(0) = 1.
A289271(2) = 1, hence a(1) = 2.
A289271(3) = 2, hence a(2) = 3.
A289271(4) = 4, hence a(4) = 4.
A289271(5) = 8, hence a(8) = 5.
A289271(6) = 3, hence a(3) = 6.
A289271(7) = 16, hence a(16) = 7.
A289271(8) = 32, hence a(32) = 8.
A289271(9) = 64, hence a(64) = 9.
A289271(10) = 5, hence a(5) = 10.
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 0..10000
• Rémy Sigrist, PARI program for A289272
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Cf. A000120, A000961, A001221, A002110, A034684, A088860, A278568, A289271 (inverse), A322989, A322990, A322991, A322992.

Cf. also A005940, A163511, A052330.

Programs

PARI

See Links section.

PARI

A289272(n) = { my(m=1, pp=1); while(n>0, pp++; while(!isprimepower(pp)||(gcd(pp,m)>1), pp++); if(n%2, m *= pp); n >>=1); (m); }; \\ Antti Karttunen, Jan 01 2019