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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
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)
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
KEYWORD
nonn,base,look
AUTHOR
Rémy Sigrist, Jun 30 2017
STATUS
approved