A323372 Lexicographically earliest sequence such that for all i, j, a(i) = a(j) => A003557(i) = A003557(j) and A323363(i) = A323363(j).

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 32, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 44, 49, 50, 51, 44, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 58, 62, 29, 65, 66, 67, 68, 69, 58, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 79

Offset

1,2

Comments

Restricted growth sequence transform of ordered pair [A003557(n), A323363(n)].

For all i, j:

a(i) = a(j) => A291751(i) = A291751(j),

a(i) = a(j) => A323364(i) = A323364(j).

Links

Antti Karttunen, Table of n, a(n) for n = 1..65537

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; };
DirInverse(v) = { my(u=vector(#v)); u[1] = (1/v[1]); for(n=2, #v, u[n] = -sumdiv(n, d, if(d<n, v[n/d]*u[d], 0))); (u) }; \\ Compute the Dirichlet inverse of the sequence given in input vector v.
A001615(n) = (n * sumdivmult(n, d, issquarefree(d)/d)); \\ From A001615
v323363 = DirInverse(vector(up_to, n, A001615(n)));
A323363(n) = v323363[n];
A003557(n) = { my(f=factor(n)); for(i=1, #f~, f[i, 2] = f[i, 2]-1); factorback(f); };
v323372 = rgs_transform(vector(up_to, n, [A003557(n), A323363(n)]));
A323372(n) = v323372[n];

Crossrefs

Cf. A001615, A003557, A291750, A291751, A323363, A323364.

Sequence in context: A295888 A295880 A296090 * A295300 A139179 A262437

Adjacent sequences: A323369 A323370 A323371 * A323373 A323374 A323375

Keyword

nonn

Author

Antti Karttunen, Jan 13 2019

Status

approved