A327162 Lexicographically earliest sequence such that for all i, j, a(i) = a(j) => f(i) = f(j), where f(n) = A034460(n) * (-1)^[A327159(n)>0], and A034460(n) = usigma(n)-n, with usigma the sum of unitary divisors of n (A034448).

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

Offset

1,2

Comments

For all i, j:

A305800(i) = A305800(j) => a(i) = a(j) => A318882(i) = A318882(j).

Links

Antti Karttunen, Table of n, a(n) for n = 1..87360

Prog

(PARI)
up_to = 87360;
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; };
A034460(n) = (sumdivmult(n, d, if(gcd(d, n/d)==1, d))-n); \\ From A034460
A327159(n, orgn=n, xs=Set([])) = if(1==n, 0, if(vecsearch(xs, n), if(n==orgn, length(xs), 0), xs = setunion([n], xs); A327159(A034460(n), orgn, xs)));
Aux327162(n) = A034460(n)*((-1)^((A327159(n)>0)));
v327162 = rgs_transform(vector(up_to, n, Aux327162(n)));
A327162(n) = v327162[n];

Crossrefs

Cf. A034448, A034460, A305800, A318882, A327159,

Sequence in context: A316990 A359212 A320018 * A326193 A327163 A324538

Adjacent sequences: A327159 A327160 A327161 * A327163 A327164 A327165

Keyword

nonn

Author

Antti Karttunen, Aug 28 2019

Status

approved