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Restricted growth sequence transform of A305814, a filter sequence constructed from the GF(2)[X]-factorization signatures of the divisors of n.

<a href="/index/Ge#GF2X">Index entries for sequences operating on GF(2)[X]-polynomials</a>

Cf. also A305795.

Antti Karttunen, <a href="/A305815/b305815.txt">Table of n, a(n) for n = 1..65537</a>

For all i, j:

a(i) = a(j) => A000005(i) = A000005(j).

a(i) = a(j) => A294883(i) = A294883(j).

a(i) = a(j) => A294884(i) = A294884(j).

allocated for Antti KarttunenRestricted growth sequence transform of A305814,

1, 2, 2, 3, 4, 5, 2, 6, 7, 8, 2, 9, 2, 5, 6, 10, 11, 12, 2, 13, 14, 5, 15, 16, 3, 5, 17, 9, 15, 16, 2, 18, 5, 19, 20, 21, 2, 5, 22, 23, 2, 24, 15, 9, 25, 26, 2, 27, 7, 9, 28, 9, 15, 29, 14, 16, 22, 26, 2, 30, 2, 5, 9, 31, 32, 33, 2, 34, 20, 35, 15, 36, 2, 5, 37, 9, 5, 38, 15, 39, 40, 5, 41, 42, 43, 26, 5, 16, 15, 44, 45, 46, 5, 5, 8, 47, 2, 12, 48, 49, 41, 50

1,2

(PARI)

\\ Needs also code from A305788:

up_to = 65537;

rgs_transform(invec) = { my(occurrences = Map(), outvec = vector(length(invec)), u=1); for(i=1, length(invec), if(mapisdefined(occurrences, invec[i]), my(pp = mapget(occurrences, invec[i])); outvec[i] = outvec[pp] , mapput(occurrences, invec[i], i); outvec[i] = u; u++ )); outvec; };

A305814(n) = { my(m=1); fordiv(n, d, if(d>1, m *= prime(A305788(d)-1))); (m); };

v305815 = rgs_transform(vector(up_to, n, A305814(n)));

A305815(n) = v305815[n];

Cf. A278233, A305788, A305813, A305814.

allocated

nonn

Antti Karttunen, Jun 11 2018

approved

editing

allocated for Antti Karttunen

allocated

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