A350062 -id:A350062 - cp's OEIS frontend

A350064 Lexicographically earliest infinite sequence such that a(i) = a(j) => A350062(i) = A350062(j), for all i, j >= 1.

1, 2, 3, 3, 4, 3, 5, 3, 6, 4, 7, 3, 8, 3, 6, 6, 9, 3, 10, 3, 11, 6, 12, 3, 11, 6, 6, 6, 13, 6, 14, 3, 6, 6, 11, 5, 15, 3, 16, 6, 17, 3, 18, 3, 6, 19, 20, 3, 19, 4, 16, 3, 21, 3, 22, 3, 16, 11, 23, 3, 24, 6, 6, 11, 11, 6, 25, 6, 6, 3, 26, 6, 27, 6, 6, 6, 19, 6, 28, 3, 16, 6, 29, 11, 30, 16, 31, 19, 32, 11, 33, 6, 30, 30, 30

Offset: 1

Antti Karttunen, Jan 29 2022

nonn

Restricted growth sequence transform of A350062.
For all i, j >= 1: a(i) = a(j) => A324105(i) = A324105(j).
For all i, j >= 2:
  a(i) = a(j) => A324119(i) = A324119(j),
  a(i) = a(j) => A342655(i) = A342655(j).

Antti Karttunen, Table of n, a(n) for n = 1..10000 (based on Hans Havermann's factorization of A156552)
Index entries for sequences computed from indices in prime factorization

Cf. A046523, A156552, A350062, A350065.

Cf. also A286621, A324105, A324119, A342655.

up_to = 3000;
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; };
A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };  \\ From A046523
A156552(n) = { my(f = factor(n), p, p2 = 1, res = 0); for(i = 1, #f~, p = 1 << (primepi(f[i, 1]) - 1); res += (p * p2 * (2^(f[i, 2]) - 1)); p2 <<= f[i, 2]); res };
A350062(n) = if(1==n,0,A046523(A156552(n)));
v350064 = rgs_transform(vector(up_to, n, A350062(n)));
A350064(n) = v350064[n];

A350063 a(n) is the smallest number with the same prime signature as A322993(n), with a(1) = 0.

Original entry on oeis.org

0, 1, 1, 2, 1, 2, 1, 2, 2, 4, 1, 2, 1, 2, 2, 6, 1, 2, 1, 2, 4, 6, 1, 2, 2, 6, 2, 6, 1, 6, 1, 2, 2, 6, 2, 8, 1, 2, 6, 6, 1, 2, 1, 2, 2, 24, 1, 2, 2, 4, 6, 2, 1, 2, 4, 2, 6, 12, 1, 2, 1, 6, 2, 12, 2, 6, 1, 6, 2, 2, 1, 6, 1, 6, 2, 6, 2, 6, 1, 2, 6, 6, 1, 12, 6, 30, 24, 24, 1, 12, 4, 6, 12, 60, 6, 6, 1, 4, 6, 6, 1

Offset: 1

Antti Karttunen, Jan 29 2022

nonn

Index entries for sequences computed from indices in prime factorization

Cf. A000265, A046523, A156552, A322993, A350062, A350064, A350065 (rgs-transform).

A000265(n) = (n>>valuation(n,2));
A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };  \\ From A046523
A156552(n) = { my(f = factor(n), p, p2 = 1, res = 0); for(i = 1, #f~, p = 1 << (primepi(f[i, 1]) - 1); res += (p * p2 * (2^(f[i, 2]) - 1)); p2 <<= f[i, 2]); res };
A350063(n) = if(1==n,0,A046523(A000265(A156552(n))));

a(1) = 0; for n > 1, a(n) = A046523(A322993(n)) = A046523(A000265(A156552(n))).

cp's OEIS Frontend

A350064 Lexicographically earliest infinite sequence such that a(i) = a(j) => A350062(i) = A350062(j), for all i, j >= 1.

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