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A323904
Lexicographically earliest sequence such that a(i) = a(j) => A033879(i) = A033879(j) and A083254(i) = A083254(j), for all i, j >= 1.
2
1, 2, 3, 2, 4, 5, 6, 2, 7, 8, 9, 10, 11, 12, 13, 2, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 2, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 38, 50, 51, 52, 53, 54, 55, 56, 57, 35, 2, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80
OFFSET
1,2
COMMENTS
Restricted growth sequence transform of the ordered pair [A033879(n), A083254(n)], the deficiency of n, and its Möbius transform.
For all i, j: a(i) = a(j) => A297159(i) = A297159(j).
LINKS
FORMULA
a(2^n) = 2 for all n >= 1.
EXAMPLE
For n=39, we have A033879(39) = 2*39 - A000203(39) = 22, and A083254(39) = 2*A000010(39)-39 = 9. For n=63 the results are same, with A033879(63) = 22 and A083254(63) = 9, thus a(39) and a(63) are allotted the same number by the restricted growth sequence transform, which in this case is 35, thus a(39) = a(63) = 35.
For n=42 and 54, we have A033879(42) = -12, A083254(42) = -18 and A033879(54) = -12, A083254(54) = -18, thus a(42) = a(54) (= 38).
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; };
A033879(n) = (2*n-sigma(n));
A083254(n) = (2*eulerphi(n)-n);
A323904aux(n) = [A033879(n), A083254(n)];
v323904 = rgs_transform(vector(up_to, n, A323904aux(n)));
A323904(n) = v323904[n];
CROSSREFS
KEYWORD
nonn
AUTHOR
Antti Karttunen, Feb 10 2019
STATUS
approved