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.

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

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 A366293 A293442

Adjacent sequences: A317940 A317941 A317942 * A317944 A317945 A317946

Keyword

nonn

Author

Antti Karttunen, Aug 12 2018

Status

approved