A331298 -id:A331298 - cp's OEIS frontend

A331297 Lexicographically earliest infinite sequence such that a(i) = a(j) => A263297(i) = A263297(j) and A325225(i) = A325225(j) for all i, j.

1, 2, 3, 3, 4, 5, 6, 4, 5, 7, 8, 7, 9, 10, 7, 6, 11, 7, 12, 13, 10, 14, 15, 10, 7, 16, 7, 17, 18, 13, 19, 8, 14, 20, 10, 10, 21, 22, 16, 17, 23, 17, 24, 25, 13, 26, 27, 14, 10, 13, 20, 28, 29, 10, 14, 30, 22, 31, 32, 17, 33, 34, 17, 9, 16, 25, 35, 36, 26, 17, 37, 14, 38, 39, 13, 40, 14, 28, 41, 25, 10, 42, 43, 30, 20, 44, 31, 45, 46, 17, 16, 47, 34, 48, 22, 16, 49, 17, 25, 17

Offset: 1

Antti Karttunen, Jan 18 2020

nonn

Restricted growth sequence transform of the unordered pair [A001222(n), A061395(n)].

Antti Karttunen, Table of n, a(n) for n = 1..65537
Index entries for sequences computed from indices in prime factorization

Cf. A001222, A061395, A263297, A325225, A331170, A331298, A331299.

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; };
A061395(n) = if(1==n, 0, primepi(vecmax(factor(n)[, 1])));
Aux331297(n) = { my(a=bigomega(n),b=A061395(n)); [min(a,b),max(a,b)]; };
Aux331297(n) = Set([bigomega(n),A061395(n)]); \\ Alternatively.
v331297 = rgs_transform(vector(up_to, n, Aux331297(n)));
A331297(n) = v331297[n];

For all i, j:
  A331170(i) = A331170(j) => a(i) = a(j),
  A331298(i) = A331298(j) => a(i) = a(j),
  A331299(i) = A331299(j) => a(i) = a(j),
  a(i) = a(j) => A326846(i) = A326846(j).

A331295 Number of values of k, 1 <= k <= n, with f(k) = f(n), where f(n) = [A001222(n), A061395(n)].

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 1, 3, 1, 3, 1, 1, 2, 1, 1, 2, 1, 3, 2, 1, 1, 2, 1, 1, 2, 1, 1, 3, 1, 1, 1, 4, 4, 2, 1, 1, 3, 3, 1, 2, 1, 1, 2, 1, 1, 3, 1, 3, 2, 1, 1, 2, 4, 1, 2, 1, 1, 5, 1, 4, 2, 1, 1, 4, 1, 1, 2, 3, 1, 2, 1, 1, 3, 4, 1, 2, 1, 3, 1, 1, 5, 3, 4, 1, 2, 1, 1, 6

Offset: 1

Antti Karttunen, Jan 19 2020

nonn

Ordinal transform of A331298, or equally, of the ordered pair [A001222(n), A061395(n)].

Antti Karttunen, Table of n, a(n) for n = 1..12000
Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537
Index entries for sequences computed from indices in prime factorization

Cf. A001222, A061395, A078899, A331296, A331297, A331298.

f[n_] := f[n] = {PrimeOmega[n], PrimePi[FactorInteger[n]][[-1, 1]]};
a[n_] := Count[Array[f, n], f[n]];
Array[a, 105] (* Jean-François Alcover, Jan 10 2022 *)

up_to = 1001;
ordinal_transform(invec) = { my(om = Map(), outvec = vector(length(invec)), pt); for(i=1, length(invec), if(mapisdefined(om,invec[i]), pt = mapget(om, invec[i]), pt = 0); outvec[i] = (1+pt); mapput(om,invec[i],(1+pt))); outvec; };
A061395(n) = if(1==n, 0, primepi(vecmax(factor(n)[, 1])));
Aux331298(n) = [bigomega(n), A061395(n)];
v331295 = ordinal_transform(vector(up_to, n, Aux331298(n)));
A331295(n) = v331295[n];

cp's OEIS Frontend

A331297 Lexicographically earliest infinite sequence such that a(i) = a(j) => A263297(i) = A263297(j) and A325225(i) = A325225(j) for all i, j.

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