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A317943 Filter sequence constructed from the coefficients of the Stern polynomials B(d,t) collected for each proper divisor d of n; Restricted growth sequence transform of A317942.

%I A317943 #12 Aug 12 2018 21:25:49
%S A317943 1,2,2,3,2,4,2,5,6,7,2,8,2,9,10,11,2,12,2,13,14,15,2,16,17,18,19,20,2,
%T A317943 21,2,22,23,24,25,26,2,27,28,29,2,30,2,31,32,33,2,34,35,36,37,38,2,39,
%U A317943 40,41,42,43,2,44,2,45,46,47,48,49,2,50,51,52,2,53,2,54,55,56,57,58,2,59,60,61,2,62,63,64,65,66,2,67,68,69,70,71,72,73,2,74,75,76,2,77,2,78,79,80,2,81,2,82,83,84,2,85,86,87,88,89,90,91,92,93,94,95,86
%N A317943 Filter sequence constructed from the coefficients of the Stern polynomials B(d,t) collected for each proper divisor d of n; Restricted growth sequence transform of A317942.
%C A317943 For all i, j: a(i) = a(j) => A317837(i) = A317837(j).
%H A317943 Antti Karttunen, <a href="/A317943/b317943.txt">Table of n, a(n) for n = 1..65537</a>
%H A317943 <a href="/index/St#Stern">Index entries for sequences related to Stern's sequences</a>
%e A317943 Proper divisors of 115 are 1, 5 and 23 and proper divisors of 125 are 1, 5 and 25. The divisors 1 and 5 occur in both, while for the Stern polynomials B(23,t) and B(25,t) (see A125184) the nonzero coefficients are {1, 2, 3, 1} and {1, 3, 2, 1}, that is, they are equal as multisets, thus A286378(23) = A286378(25). From this follows that a(115) = a(125).
%o A317943 (PARI)
%o A317943 \\ Needs also code from A286378:
%o A317943 up_to = 65537;
%o A317943 A317942(n) = { my(m=1); fordiv(n,d,if(d<n, m *= prime(A286378(d)-1))); (m); };
%o A317943 v317943 = rgs_transform(vector(up_to, n, A317942(n)));
%o A317943 A317943(n) = v317943[n];
%Y A317943 Cf. A125184, A286378, A317837, A317942, A317945.
%Y A317943 Cf. also A293217, A305793.
%Y A317943 Differs from A305800 and A296073 for the first time at n=125, where a(125) = 86.
%K A317943 nonn
%O A317943 1,2
%A A317943 _Antti Karttunen_, Aug 12 2018