This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A283477 #75 Dec 08 2022 11:55:23
%S A283477 1,2,6,12,30,60,180,360,210,420,1260,2520,6300,12600,37800,75600,2310,
%T A283477 4620,13860,27720,69300,138600,415800,831600,485100,970200,2910600,
%U A283477 5821200,14553000,29106000,87318000,174636000,30030,60060,180180,360360,900900,1801800,5405400,10810800,6306300,12612600,37837800,75675600
%N A283477 If 2n = 2^e1 + 2^e2 + ... + 2^ek [e1 .. ek distinct], then a(n) = A002110(e1) * A002110(e2) * ... * A002110(ek).
%C A283477 a(n) = Product of distinct primorials larger than one, obtained as Product_{i} A002110(1+i), where i ranges over the zero-based positions of the 1-bits present in the binary representation of n.
%C A283477 This sequence can be represented as a binary tree. Each child to the left is obtained as A283980(k), and each child to the right is obtained as 2*A283980(k), when their parent contains k:
%C A283477 1
%C A283477 |
%C A283477 ...................2....................
%C A283477 6 12
%C A283477 30......../ \........60 180......../ \......360
%C A283477 / \ / \ / \ / \
%C A283477 / \ / \ / \ / \
%C A283477 / \ / \ / \ / \
%C A283477 210 420 1260 2520 6300 12600 37800 75600
%C A283477 etc.
%H A283477 Antti Karttunen, <a href="/A283477/b283477.txt">Table of n, a(n) for n = 0..4095</a>
%H A283477 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%H A283477 <a href="/index/Pri#primorial_numbers">Index entries for sequences related to primorial numbers</a>
%F A283477 a(0) = 1; a(2n) = A283980(a(n)), a(2n+1) = 2*A283980(a(n)).
%F A283477 Other identities. For all n >= 0 (or for n >= 1):
%F A283477 a(2n+1) = 2*a(2n).
%F A283477 a(n) = A108951(A019565(n)).
%F A283477 A097248(a(n)) = A283475(n).
%F A283477 A007814(a(n)) = A051903(a(n)) = A000120(n).
%F A283477 A001221(a(n)) = A070939(n).
%F A283477 A001222(a(n)) = A029931(n).
%F A283477 A048675(a(n)) = A005187(n).
%F A283477 A248663(a(n)) = A006068(n).
%F A283477 A090880(a(n)) = A283483(n).
%F A283477 A276075(a(n)) = A283984(n).
%F A283477 A276085(a(n)) = A283985(n).
%F A283477 A046660(a(n)) = A124757(n).
%F A283477 A056169(a(n)) = A065120(n). [seems to be]
%F A283477 A005361(a(n)) = A284001(n).
%F A283477 A072411(a(n)) = A284002(n).
%F A283477 A007913(a(n)) = A284003(n).
%F A283477 A000005(a(n)) = A284005(n).
%F A283477 A324286(a(n)) = A324287(n).
%F A283477 A276086(a(n)) = A324289(n).
%F A283477 A267263(a(n)) = A324341(n).
%F A283477 A276150(a(n)) = A324342(n). [subsequences in the latter are converging towards this sequence]
%F A283477 G.f.: Product_{k>=0} (1 + prime(k + 1)# * x^(2^k)), where prime()# = A002110. - _Ilya Gutkovskiy_, Aug 19 2019
%t A283477 Table[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, 43}] (* _Michael De Vlieger_, Mar 18 2017 *)
%o A283477 (PARI) A283477(n) = prod(i=0,exponent(n),if(bittest(n,i),vecprod(primes(1+i)),1)) \\ Edited by _M. F. Hasler_, Nov 11 2019
%o A283477 (Scheme)
%o A283477 (define (A283477 n) (A108951 (A019565 n)))
%o A283477 ;; Recursive "binary tree" implementation, using memoization-macro definec:
%o A283477 (definec (A283477 n) (cond ((zero? n) 1) ((even? n) (A283980 (A283477 (/ n 2)))) (else (* 2 (A283980 (A283477 (/ (- n 1) 2)))))))
%o A283477 (Python)
%o A283477 from sympy import prime, primerange, factorint
%o A283477 from operator import mul
%o A283477 from functools import reduce
%o A283477 def P(n): return reduce(mul, [i for i in primerange(2, n + 1)])
%o A283477 def a108951(n):
%o A283477 f = factorint(n)
%o A283477 return 1 if n==1 else reduce(mul, [P(i)**f[i] for i in f])
%o A283477 def a019565(n): return reduce(mul, (prime(i+1) for i, v in enumerate(bin(n)[:1:-1]) if v == '1')) if n > 0 else 1 # after _Chai Wah Wu_
%o A283477 def a(n): return a108951(a019565(n))
%o A283477 print([a(n) for n in range(101)]) # _Indranil Ghosh_, Jun 22 2017
%o A283477 (Python)
%o A283477 from sympy import primorial
%o A283477 from math import prod
%o A283477 def A283477(n): return prod(primorial(i) for i, b in enumerate(bin(n)[:1:-1],1) if b =='1') # _Chai Wah Wu_, Dec 08 2022
%Y A283477 Cf. A129912 (same terms, but sorted into ascending order).
%Y A283477 Cf. A000120, A001221, A001222, A002110, A005187, A005361, A006068, A007814, A007913, A019565, A029931, A030308, A046660, A048675, A051903, A056169, A065120, A070939, A072411, A090880, A097248, A108951, A124757, A248663, A276075, A276085, A283475, A283483, A283980, A283984, A283985, A284001, A284002, A284003, A284005, A324287, A324289, A324341, A324342, A324343.
%Y A283477 Cf. A005940, A052330, A322827, A323505 for other similar trees.
%Y A283477 Cf. also A260443.
%K A283477 nonn
%O A283477 0,2
%A A283477 _Antti Karttunen_, Mar 16 2017
%E A283477 More formulas and the binary tree illustration added by _Antti Karttunen_, Mar 19 2017
%E A283477 Four more linking formulas added by _Antti Karttunen_, Feb 25 2019