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A289272 Inverse to A289271. 9
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

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)

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

EXAMPLE

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.

PROG

(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

CROSSREFS

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

Cf. also A005940, A163511, A052330.

Sequence in context: A320123 A194357 A165783 * A073318 A254047 A049449

Adjacent sequences:  A289269 A289270 A289271 * A289273 A289274 A289275

KEYWORD

nonn,base,look

AUTHOR

Rémy Sigrist, Jun 30 2017

STATUS

approved

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Last modified March 4 08:38 EST 2021. Contains 341781 sequences. (Running on oeis4.)