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A275733 a(0) = 1; for n >= 1, a(n) = A275732(n) * A003961(a(A257684(n))).

%I A275733 #26 Mar 12 2025 07:39:56
%S A275733 1,2,3,6,3,6,5,10,15,30,15,30,5,10,15,30,15,30,5,10,15,30,15,30,7,14,
%T A275733 21,42,21,42,35,70,105,210,105,210,35,70,105,210,105,210,35,70,105,
%U A275733 210,105,210,7,14,21,42,21,42,35,70,105,210,105,210,35,70,105,210,105,210,35,70,105,210,105,210,7,14,21,42,21,42
%N A275733 a(0) = 1; for n >= 1, a(n) = A275732(n) * A003961(a(A257684(n))).
%C A275733 a(n) = product of primes whose indices are positions of nonzero-digits in factorial base representation of n (see A007623). Here positions are one-based, so that the least significant digit is the position 1, the next least significant the position 2, etc.
%H A275733 Antti Karttunen, <a href="/A275733/b275733.txt">Table of n, a(n) for n = 0..40320</a>
%H A275733 Indranil Ghosh, <a href="/A275733/a275733.txt">Python program for computing this sequence</a>
%H A275733 <a href="/index/Fa#facbase">Index entries for sequences related to factorial base representation</a>
%F A275733 a(0) = 1; for n >= 1, a(n) = A275732(n) * A003961(a(A257684(n))).
%F A275733 Other identities and observations. For all n >= 0:
%F A275733 a(A007489(n)) = A002110(n).
%F A275733 A001221(a(n)) = A001222(a(n)) = A060130(n).
%F A275733 A048675(a(n)) = A275727(n).
%F A275733 A061395(a(n)) = A084558(n).
%e A275733 For n=19, A007623(19) = 301, thus a(19) = prime(3)*prime(1) = 5*2 = 10.
%e A275733 For n=52, A007623(52) = 2020, thus a(52) = prime(2)*prime(4) = 3*7 = 21.
%o A275733 (Scheme, with memoization-macro definec)
%o A275733 (definec (A275733 n) (if (zero? n) 1 (* (A275732 n) (A003961 (A275733 (A257684 n))))))
%Y A275733 Cf. A001221, A002110, A003961, A005117, A007489, A007623, A048675, A060130, A061395, A084558, A257684, A275732.
%Y A275733 Subsequence of A005117.
%Y A275733 Cf. A275727.
%Y A275733 Cf. also A275725, A275734, A275735 for other such prime factorization encodings of A060117/A060118-related polynomials.
%K A275733 nonn,base
%O A275733 0,2
%A A275733 _Antti Karttunen_, Aug 08 2016