A336393 -id:A336393 - cp's OEIS frontend

A336390 Lexicographically earliest infinite sequence such that a(i) = a(j) => A336467(i) = A336467(j) and A336158(i) = A336158(j), for all i, j >= 1.

1, 1, 2, 1, 3, 2, 2, 1, 4, 3, 3, 2, 5, 2, 6, 1, 7, 4, 8, 3, 9, 3, 3, 2, 10, 5, 11, 2, 12, 6, 2, 1, 6, 7, 6, 4, 13, 8, 14, 3, 15, 9, 16, 3, 17, 3, 3, 2, 4, 10, 18, 5, 19, 11, 18, 2, 20, 12, 12, 6, 21, 2, 22, 1, 23, 6, 24, 7, 6, 6, 7, 4, 25, 13, 26, 8, 6, 14, 8, 3, 27, 15, 15, 9, 28, 16, 29, 3, 30, 17, 14, 3, 9, 3, 29, 2, 31, 4, 17, 10, 32, 18, 33, 5, 34

Offset: 1

Antti Karttunen, Aug 10 2020

nonn

Restricted growth sequence transform of the ordered pair [A336467(n), A336158(n)].
For all i, j:
  A324400(i) = A324400(j) => A003602(i) = A003602(j) => a(i) = a(j),
  a(i) = a(j) => A331410(i) = A331410(j),
  a(i) = a(j) => A336391(i) = A336391(j).

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

Cf. A003602, A324400, A336158, A336467, A336391, A336393.

Cf. also A336470.

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; };
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
A336158(n) = A046523(A000265(n));
A336467(n) = { my(f=factor(n)); prod(k=1,#f~,if(2==f[k,1],1,(A000265(f[k,1]+1))^f[k,2])); };
Aux336390(n) = [A336158(n), A336467(n)];
v336390 = rgs_transform(vector(up_to, n, Aux336390(n)));
A336390(n) = v336390[n];

A336395 Lexicographically earliest infinite sequence such that a(i) = a(j) => A278221(A000265(i)) = A278221(A000265(j)), for all i, j >= 1.

Original entry on oeis.org

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

Offset: 1

Antti Karttunen, Aug 10 2020

nonn

Restricted growth sequence transform of the function f(n) = A278221(A000265(n)), the prime signature of the conjugated prime factorization of the odd part of n.
For all i, j:
  A324400(i) = A324400(j) => A003602(i) = A003602(j) => a(i) = a(j),
  a(i) = a(j) => A005087(i) = A005087(j).

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

Cf. A000265, A003602, A005087, A278221, A286621, A324400.

Cf. also A336393.

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; };
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
A122111(n) = if(1==n,n,my(f=factor(n), es=Vecrev(f[,2]),is=concat(apply(primepi,Vecrev(f[,1])),[0]),pri=0,m=1); for(i=1, #es, pri += es[i]; m *= prime(pri)^(is[i]-is[1+i])); (m));
A278221(n) = A046523(A122111(n));
v336395 = rgs_transform(vector(up_to, n, A278221(A000265(n))));
A336395(n) = v336395[n];

cp's OEIS Frontend

A336390 Lexicographically earliest infinite sequence such that a(i) = a(j) => A336467(i) = A336467(j) and A336158(i) = A336158(j), for all i, j >= 1.

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