A351090 -id:A351090 - cp's OEIS frontend

A351037 Lexicographically earliest infinite sequence such that a(i) = a(j) => A000593(i) = A000593(j), for all i, j >= 1, where A000593 is the sum of odd divisors function.

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

Offset: 1

Antti Karttunen, Jan 31 2022

Restricted growth sequence transform of A000593.

Question: To which set of n does the horizontal stripe at around a(n) = ~8000 correspond in the scatter plot of this sequence?

			a(21) = a(31) = 11 because A000593(21) = A000593(31) = 32, and 32 is the 11th distinct value obtained by A000593.

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

Cf. A000593.

Cf. also A286603, A347374, A351036, A351040, A351090.

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; };
v351037 = rgs_transform(vector(up_to, n, sigma(n>>valuation(n,2))));
A351037(n) = v351037[n];

A365388 Lexicographically earliest infinite sequence such that a(i) = a(j) => A334867(i) = A334867(i) and A365386(j) = A365386(j) for all i, j >= 1.

Original entry on oeis.org

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

Offset: 1

Antti Karttunen, Sep 07 2023

nonn

Restricted growth sequence transform of the ordered pair [A334867(n), A365386(n)], or equally, of the quadruplet [A329697(n), A334204(n), A331410(n), A365385(n)].
For all i, j:
  A003602(i) = A003602(j) => a(i) = a(j),
  a(i) = a(j) => A334867(i) = A334867(j),
  a(i) = a(j) => A335880(i) = A335880(j),
  a(i) = a(j) => A365386(i) = A365386(j).

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

Cf. A163511, A329697, A331410, A334204, A334867, A335880, A365385, A365386.

Differs from A003602 and A351090 for the first time at n=99, where a(99) = 41, while A003602(99) = A351090(99) = 50.

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; };
A163511(n) = if(!n, 1, my(p=2, t=1); while(n>1, if(!(n%2), (t*=p), p=nextprime(1+p)); n >>= 1); (t*p));
A329697(n) = if(!bitand(n,n-1),0,1+A329697(n-(n/vecmax(factor(n)[, 1]))));
A334204(n) = A329697(A163511(n));
A331410(n) = if(!bitand(n,n-1),0,1+A331410(n+(n/vecmax(factor(n)[, 1]))));
A365385(n) = A331410(A163511(n));
A365388aux(n) = [A329697(n),A334204(n),A331410(n),A365385(n)];
v365388 = rgs_transform(vector(up_to,n,A365388aux(n)));
A365388(n) = v365388[n];

A351093 Lexicographically earliest infinite sequence such that a(i) = a(j) => A351091(i) = A351091(j), for all i, j >= 1.

Original entry on oeis.org

1, 1, 2, 1, 2, 2, 3, 1, 4, 2, 5, 2, 6, 3, 7, 1, 5, 4, 3, 2, 8, 5, 2, 2, 9, 6, 10, 3, 11, 7, 12, 1, 10, 5, 12, 4, 13, 3, 14, 2, 10, 8, 13, 5, 15, 2, 11, 2, 16, 9, 10, 6, 11, 10, 6, 3, 8, 11, 2, 7, 3, 12, 17, 1, 17, 10, 6, 5, 7, 12, 5, 4, 3, 13, 18, 3, 6, 14, 3, 2, 19, 10, 20, 8, 21, 13, 22, 5, 20, 15, 23, 2, 24, 11

Offset: 1

Antti Karttunen, Jan 31 2022

Restricted growth sequence transform of A351091.

Antti Karttunen, Table of n, a(n) for n = 1..20000

Cf. A351090, A351091, A351094.

up_to = 20000;
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; };
A019565(n) = { my(m=1, p=1); while(n>0, p = nextprime(1+p); if(n%2, m *= p); n >>= 1); (m); };
A289813(n) = { my(d=digits(n, 3)); fromdigits(vector(#d, i, if (d[i]==1, 1, 0)), 2); }; \\ From A289813
A351091(n) = { my(m=1); fordiv(n>>valuation(n,2),d,m *= A019565(A289813(d))); (m); };
v351093 = rgs_transform(vector(up_to, n, A351091(n)));
A351093(n) = v351093[n];

A351094 Lexicographically earliest infinite sequence such that a(i) = a(j) => A351092(i) = A351092(j), for all i, j >= 1.

Original entry on oeis.org

1, 1, 1, 1, 2, 1, 3, 1, 1, 2, 2, 1, 1, 3, 4, 1, 4, 1, 5, 2, 6, 2, 7, 1, 8, 1, 1, 3, 2, 4, 1, 1, 4, 4, 9, 1, 1, 5, 1, 2, 2, 6, 3, 2, 8, 7, 7, 1, 6, 8, 10, 1, 8, 1, 11, 3, 12, 2, 13, 4, 14, 1, 15, 1, 11, 4, 16, 4, 17, 9, 18, 1, 12, 1, 19, 5, 20, 1, 15, 2, 1, 2, 2, 6, 21, 3, 4, 2, 4, 8, 3, 7, 1, 7, 22, 1, 3, 6, 8, 8

Offset: 1

Antti Karttunen, Jan 31 2022

Restricted growth sequence transform of A351092.

Antti Karttunen, Table of n, a(n) for n = 1..20000

Cf. A351090, A351092, A351093.

up_to = 20000;
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; };
A019565(n) = { my(m=1, p=1); while(n>0, p = nextprime(1+p); if(n%2, m *= p); n >>= 1); (m); };
A289814(n) = { my(d=digits(n, 3)); fromdigits(vector(#d, i, if (d[i]==2, 1, 0)), 2); }; \\ From A289814
A351092(n) = { my(m=1); fordiv(n>>valuation(n,2),d,m *= A019565(A289814(d))); (m); };
v351094 = rgs_transform(vector(up_to, n, A351092(n)));
A351094(n) = v351094[n];

A366380 Lexicographically earliest infinite sequence such that a(i) = a(j) => A336158(i) = A336158(j), A336466(i) = A336466(j) and A336467(i) = A336467(j) for all i, j >= 1, where A336466 is fully multiplicative with a(p) = oddpart(p-1) for any prime p and A336467 is fully multiplicative with a(2) = 1 and a(p) = oddpart(p+1) for odd primes, and A336158(n) gives the prime signature of the odd part of n.

Original entry on oeis.org

1, 1, 2, 1, 3, 2, 4, 1, 5, 3, 6, 2, 7, 4, 8, 1, 9, 5, 10, 3, 11, 6, 12, 2, 13, 7, 14, 4, 15, 8, 16, 1, 17, 9, 18, 5, 19, 10, 20, 3, 21, 11, 22, 6, 23, 12, 24, 2, 25, 13, 26, 7, 27, 14, 28, 4, 29, 15, 30, 8, 31, 16, 32, 1, 33, 17, 34, 9, 35, 18, 36, 5, 37, 19, 38, 10, 39, 20, 40, 3, 41, 21, 42, 11, 43, 22, 44, 6, 45, 23, 46, 12, 47, 24, 48, 2, 49, 25, 50

Offset: 1

Antti Karttunen, Oct 12 2023

nonn

Restricted growth sequence transform of the triplet [A336158(n), A336466(n), A336467(n)].
For all i, j >= 1:
  A003602(i) = A003602(j) => a(i) = a(j),
  a(i) = a(j) => A366381(i) = A366381(j),
  a(i) = a(j) => A335880(i) = A335880(j),
  a(i) = a(j) => A336390(i) = A336390(j),
  a(i) = a(j) => A336470(i) = A336470(j).

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

Cf. A000265, A003602, A335880, A336158, A336466, A336467, A336470, A336390, A366381.
Differs from A003602 and A351090 for the first time at n=153, where a(153) = 38, while A003602(153) = A351090(153) = 77.
Differs from A365388 for the first time at n=99, where a(99) = 50, while A365388(99) = 41.

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));
A336466(n) = { my(f=factor(n)); prod(k=1, #f~, A000265(f[k, 1]-1)^f[k, 2]); };
A336467(n) = { my(f=factor(n)); prod(k=1,#f~,if(2==f[k,1],1,(A000265(f[k,1]+1))^f[k,2])); };
A366380aux(n) = [A336158(n), A336466(n), A336467(n)];
v366380 = rgs_transform(vector(up_to,n,A366380aux(n)));
A366380(n) = v366380[n];

cp's OEIS Frontend

A351037 Lexicographically earliest infinite sequence such that a(i) = a(j) => A000593(i) = A000593(j), for all i, j >= 1, where A000593 is the sum of odd divisors function.

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A365388 Lexicographically earliest infinite sequence such that a(i) = a(j) => A334867(i) = A334867(i) and A365386(j) = A365386(j) for all i, j >= 1.

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A351093 Lexicographically earliest infinite sequence such that a(i) = a(j) => A351091(i) = A351091(j), for all i, j >= 1.

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A351094 Lexicographically earliest infinite sequence such that a(i) = a(j) => A351092(i) = A351092(j), for all i, j >= 1.

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