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A332030 a(n) is the product of the distinct positive numbers whose binary digits appear in order, but not necessarily as consecutive digits, in the binary representation of n.

%I A332030 #8 Feb 08 2020 11:45:00
%S A332030 1,1,2,3,8,30,36,21,64,1080,7200,2310,1728,16380,3528,315,1024,146880,
%T A332030 9331200,1580040,13824000,1362160800,170755200,796950,331776,
%U A332030 176904000,2861913600,72972900,4741632,99754200,1587600,9765,32768,77552640,86294937600
%N A332030 a(n) is the product of the distinct positive numbers whose binary digits appear in order, but not necessarily as consecutive digits, in the binary representation of n.
%C A332030 This sequence is a variant of A165153.
%C A332030 For n > 0, a(n) is the product of the terms of the n-th row of A301983.
%H A332030 Rémy Sigrist, <a href="/A332030/b332030.txt">Table of n, a(n) for n = 0..4096</a>
%F A332030 a(n) >= A165153(n).
%F A332030 a(2^k) = A006125(k+1) for any k >= 0.
%F A332030 a(2^k-1) = A005329(k) for any k >= 0.
%e A332030 For n = 9:
%e A332030 - the binary representation of 9 is "1001",
%e A332030 - the following positive binary strings appear in it: "1", "10", "11", "100", "101" and "1001",
%e A332030 - they correspond to: 1, 2, 3, 4, 5 and 9,
%e A332030 - so a(9) = 1 * 2 * 3 * 4 * 5 * 9 = 1080.
%o A332030 (PARI) a(n) = my (b=binary(n), s=[0]); for (i=1, #b, s=setunion(s, apply(m -> 2*m+b[i], s))); vecprod(s[2..#s])
%Y A332030 Cf. A005329, A006125, A165153, A301983, A328379 (additive variant).
%K A332030 nonn,base
%O A332030 0,3
%A A332030 _Rémy Sigrist_, Feb 05 2020