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 A332382 #21 Mar 07 2022 19:35:14
%S A332382 1,3,5,15,7,21,35,105,11,33,55,165,77,231,385,1155,13,39,65,195,91,
%T A332382 273,455,1365,143,429,715,2145,1001,3003,5005,15015,17,51,85,255,119,
%U A332382 357,595,1785,187,561,935,2805,1309,3927,6545,19635,221,663,1105,3315,1547,4641,7735,23205
%N A332382 If n = Sum (2^e_k) then a(n) = Product (prime(e_k + 2)).
%C A332382 Permutation of odd squarefree numbers (A056911).
%C A332382 a(n) is the n-th power of 3 in the monoid defined in A331590. - _Peter Munn_, May 02 2020
%H A332382 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%F A332382 G.f.: Product_{k>=0} (1 + prime(k+2) * x^(2^k)).
%F A332382 a(0) = 1; a(n) = prime(floor(log_2(n)) + 2) * a(n - 2^floor(log_2(n))).
%F A332382 a(2^(k-1)-1) = A002110(k)/2 for k > 0.
%F A332382 From _Peter Munn_, May 02 2020: (Start)
%F A332382 a(2n) = A003961(a(n)).
%F A332382 a(2n+1) = 3 * a(2n).
%F A332382 a(n) = A225546(4^n).
%F A332382 a(n+k) = A331590(a(n), a(k)).
%F A332382 a(n XOR k) = A059897(a(n), a(k)), where XOR denotes bitwise exclusive-or, A003987.
%F A332382 A048675(a(n)) = 2n.
%F A332382 (End)
%F A332382 a(n+1) = A334748(a(n)). - _Peter Munn_, Mar 04 2022
%e A332382 21 = 2^0 + 2^2 + 2^4 so a(21) = prime(2) * prime(4) * prime(6) = 3 * 7 * 13 = 273.
%p A332382 a:= n-> (l-> mul(ithprime(i+1)^l[i], i=1..nops(l)))(convert(n, base, 2)):
%p A332382 seq(a(n), n=0..55); # _Alois P. Heinz_, Feb 10 2020
%t A332382 nmax = 55; CoefficientList[Series[Product[(1 + Prime[k + 2] x^(2^k)), {k, 0, Floor[Log[2, nmax]]}], {x, 0, nmax}], x]
%t A332382 a[0] = 1; a[n_] := Prime[Floor[Log[2, n]] + 2] a[n - 2^Floor[Log[2, n]]]; Table[a[n], {n, 0, 55}]
%o A332382 (PARI) a(n) = my(b=Vecrev(binary(n))); prod(k=1, #b, if (b[k], prime(k+1), 1)); \\ _Michel Marcus_, Feb 10 2020
%Y A332382 Bisection of A019565.
%Y A332382 Cf. A002110, A029930, A048675, A056911, A121663, A225546.
%Y A332382 A003961, A003987, A059897, A331590, A334748 are used to express relationship between terms of this sequence.
%K A332382 nonn
%O A332382 0,2
%A A332382 _Ilya Gutkovskiy_, Feb 10 2020