

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.


5



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, 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, 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
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OFFSET

1,2


COMMENTS

For all i, j: a(i) = a(j) => A317837(i) = A317837(j).


LINKS

Antti Karttunen, Table of n, a(n) for n = 1..65537
Index entries for sequences related to Stern's sequences


EXAMPLE

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).


PROG

(PARI)
\\ Needs also code from A286378:
up_to = 65537;
A317942(n) = { my(m=1); fordiv(n, d, if(d<n, m *= prime(A286378(d)1))); (m); };
v317943 = rgs_transform(vector(up_to, n, A317942(n)));
A317943(n) = v317943[n];


CROSSREFS

Cf. A125184, A286378, A317837, A317942, A317945.
Cf. also A293217, A305793.
Differs from A305800 and A296073 for the first time at n=125, where a(125) = 86.
Sequence in context: A320014 A319693 A296073 * A305800 A293442 A318470
Adjacent sequences: A317940 A317941 A317942 * A317944 A317945 A317946


KEYWORD

nonn


AUTHOR

Antti Karttunen, Aug 12 2018


STATUS

approved



