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 A300835 Restricted growth sequence transform of A300834, product_{d|n, d
 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, 7, 35, 36, 37, 2, 38, 39, 40, 41, 42, 2, 43, 2, 44, 45, 46, 47, 48, 2, 49, 50, 51, 2, 52, 2, 53, 54, 55, 56, 57, 2, 58, 59, 60, 2, 61, 41, 62, 63, 64, 2, 65, 66, 67, 68, 69 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS For all i, j: a(i) = a(j) => A001065(i) = A001065(j). For all i, j: a(i) = a(j) => A300836(i) = A300836(j). LINKS Antti Karttunen, Table of n, a(n) for n = 1..65537 EXAMPLE For cases n=10 and 49, we see that 10 has proper divisors 1, 2 and 5 and these have Zeckendorf-representations (A014417) 1, 10 and 1000, while 49 has proper divisors 1 and 7 and these have Zeckendorf-representations 1 and 1010. When these Zeckendorf-representations are summed (columnwise without carries), result in both cases is 1011, thus a(10) = a(49). PROG (PARI) up_to = 65537; 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])); } A072649(n) = { my(m); if(n<1, 0, m=0; until(fibonacci(m)>n, m++); m-2); }; \\ From A072649 A003714(n) = { my(s=0, w); while(n>2, w = A072649(n); s += 2^(w-1); n -= fibonacci(w+1)); (s+n); } A019565(n) = {my(j, v); factorback(Mat(vector(if(n, #n=vecextract(binary(n), "-1..1")), j, [prime(j), n[j]])~))}; \\ From A019565 A300834(n) = { my(m=1); fordiv(n, d, if(d < n, m *= A019565(A003714(d)))); m; }; write_to_bfile(1, rgs_transform(vector(up_to, n, A300834(n))), "b300835.txt"); CROSSREFS Cf. A003714, A014417, A019565, A300834, A300836. Cf. also A293215, A293217, A293223, A293224, A293232, A300833 for similar filtering sequences. Sequence in context: A300231 A293215 A293232 * A319348 A300249 A300235 Adjacent sequences:  A300832 A300833 A300834 * A300836 A300837 A300838 KEYWORD nonn AUTHOR Antti Karttunen, Mar 18 2018 STATUS approved

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Last modified September 19 04:52 EDT 2019. Contains 327187 sequences. (Running on oeis4.)