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A353522
Lexicographically earliest infinite sequence such that a(i) = a(j) => A000035(i) = A000035(j) and A003415(i) = A003415(j), for all i, j >= 1, where A000035 and A003415 compute the parity and the arithmetic derivative of their argument.
2
1, 2, 3, 4, 3, 5, 3, 6, 7, 8, 3, 9, 3, 10, 11, 12, 3, 13, 3, 14, 15, 16, 3, 17, 15, 18, 19, 12, 3, 20, 3, 21, 22, 23, 24, 25, 3, 13, 26, 27, 3, 28, 3, 29, 30, 31, 3, 32, 22, 33, 34, 35, 3, 36, 26, 37, 38, 20, 3, 37, 3, 39, 40, 41, 42, 43, 3, 44, 45, 46, 3, 47, 3, 48, 49, 21, 42, 50, 3, 51, 52, 53, 3, 54, 38, 33, 55, 56, 3, 57, 34, 58
OFFSET
1,2
COMMENTS
Restricted growth sequence transform of the ordered pair [A000035(n), A003415(n)].
For all i, j:
A353520(i) = A353520(j) => A353521(i) = A353521(j) => a(i) = a(j).
LINKS
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; };
A000035(n) = (n%2);
A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
Aux353522(n) = [A000035(n), A003415(n)];
v353522 = rgs_transform(vector(up_to, n, Aux353522(n)));
A353522(n) = v353522[n];
CROSSREFS
Cf. also A305801, A353520, A353521.
Sequence in context: A352898 A318500 A325384 * A323371 A369447 A319346
KEYWORD
nonn
AUTHOR
Antti Karttunen, Apr 27 2022
STATUS
approved