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URL: https://oeis.org/A293450

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A293450
Restricted growth sequence transform of (3*A293225(n) + A010872(n)), a filter combining (n mod 3) with two products, the other formed from the 1-digits (A293221) and the other from the 2-digits (A293222) present in the ternary expansions of proper divisors of n.
1
1, 2, 3, 4, 2, 5, 6, 7, 8, 9, 2, 10, 6, 11, 12, 13, 2, 14, 6, 15, 16, 17, 2, 18, 19, 20, 21, 22, 2, 23, 6, 24, 25, 26, 27, 28, 6, 29, 30, 31, 2, 32, 6, 33, 34, 35, 2, 36, 37, 38, 14, 39, 2, 40, 41, 42, 43, 44, 2, 45, 6, 46, 47, 48, 49, 50, 6, 51, 52, 53, 2, 54, 6, 55, 56, 57, 58, 59, 6, 60, 61, 62, 2, 63, 64, 65, 66, 67, 2
OFFSET
1,2
LINKS
FORMULA
For all i, j: a(i) = a(j) => A002324(i) = A002324(j).
PROG
(PARI)
rgs_transform(invec) = { my(om = Map(), outvec = vector(length(invec)), u=1); for(i=1, length(invec), if(mapisdefined(om, invec[i]), my(pp = mapget(om, invec[i])); outvec[i] = outvec[pp] , mapput(om, invec[i], i); outvec[i] = u; u++ )); outvec; };
write_to_bfile(start_offset, vec, bfilename) = { for(n=1, length(vec), write(bfilename, (n+start_offset)-1, " ", vec[n])); }
A019565(n) = {my(j, v); factorback(Mat(vector(if(n, #n=vecextract(binary(n), "-1..1")), j, [prime(j), n[j]])~))}; \\ This function from M. F. Hasler
A289813(n) = { my (d=digits(n, 3)); from digits(vector(#d, i, if (d[i]==1, 1, 0)), 2); };
A289814(n) = { my (d=digits(n, 3)); from digits(vector(#d, i, if (d[i]==2, 1, 0)), 2); };
A293221(n) = { my(m=1); fordiv(n, d, if(d < n, m *= A019565(A289813(d)))); m; };
A293222(n) = { my(m=1); fordiv(n, d, if(d < n, m *= A019565(A289814(d)))); m; };
Anot_submitted(n) = (1/2)*(2 + ((A293222(n) + A293221(n))^2) - A293222(n) - 3*A293221(n)); \\ Eq.class-wise equal to A293225.
Anot2submitted(n) = ((3*Anot_submitted(n))+(n%3));
write_to_bfile(1, rgs_transform(vector(59049, n, Anot2submitted(n))), "b293450.txt");
CROSSREFS
KEYWORD
nonn
AUTHOR
Antti Karttunen, Nov 06 2017
STATUS
approved