A351030 -id:A351030 - cp's OEIS frontend

A351090 Lexicographically earliest infinite sequence such that a(i) = a(j) => A351091(i) = A351091(j) and A351092(i) = A351092(j), for all i, j >= 1.

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

Offset: 1

Antti Karttunen, Jan 31 2022

Restricted growth sequence transform of the ordered pair [A351091(n), A351092(n)], or equally, of the ordered pair [A351093(n), A351094(n)].

For all i, j: A003602(i) = A003602(j) => a(i) = a(j) => A000593(i) = A000593(j).

			Consider two odd semiprimes, 689 and 697. The divisors of 689 are 1, 13, 53, 689, and the divisors of 697 are 1, 17, 41, 697. Applying A019565(A289813(x)) to the former gives [2, 30, 7, 105], while with the latter it gives [2, 5, 105, 42], and the product of both sequences is 44100. Applying A019565(A289814(x)) to the former gives [1, 1, 30, 286], while with the latter it gives [1, 6, 2, 715]. Product of both sequences is 8580. Therefore, because A351091(689) = A351091(697) and A351092(689) = A351092(697), also a(689) = a(697).

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

Cf. A000593, A351037, A351091, A351092, A351093, A351094.
Differs from A003602 for the first time at n=697, where a(697) = 345 while A003602(697) = 349.
Cf. also A293226, A351030.

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; };
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
A289814(n) = { my (d=digits(n, 3)); fromdigits(vector(#d, i, if (d[i]==2, 1, 0)), 2); }; \\ From A289814
A351091(n) = { my(m=1); fordiv(n>>valuation(n,2),d,m *= A019565(A289813(d))); (m); };
A351092(n) = { my(m=1); fordiv(n>>valuation(n,2),d,m *= A019565(A289814(d))); (m); };
Aux351090(n) = [A351091(n),A351092(n)];
v351090 = rgs_transform(vector(up_to, n, Aux351090(n)));
A351090(n) = v351090[n];

A351031 a(n) = Product_{d|n, dA019565(A304759(d)).

Original entry on oeis.org

1, 2, 2, 2, 2, 6, 2, 6, 6, 12, 2, 18, 2, 2, 36, 90, 2, 180, 2, 180, 6, 4, 2, 810, 12, 10, 180, 30, 2, 180, 2, 9450, 12, 20, 12, 56700, 2, 30, 30, 56700, 2, 420, 2, 12, 1080, 10, 2, 1275750, 2, 120, 60, 30, 2, 31500, 24, 9450, 90, 20, 2, 238140, 2, 4, 2520, 10914750, 60, 84, 2, 420, 30, 31500, 2, 2946982500, 2, 6

Offset: 1

Antti Karttunen, Jan 29 2022

nonn

Index entries for sequences computed from indices in prime factorization

Cf. A019565, A048673, A289813, A304759, A351030, A351032, A351033 (rgs-transform).

Cf. also A293221.

A019565(n) = { my(m=1, p=1); while(n>0, p = nextprime(1+p); if(n%2, m *= p); n >>= 1); (m); };
A048673(n) = { my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); (1+factorback(f))/2; };
A289813(n) = { my(d=digits(n, 3)); fromdigits(vector(#d, i, if (d[i]==1, 1, 0)), 2); } \\ From A289813
A304759(n) = A289813(A048673(n));
A351031(n) = { my(m=1); fordiv(n,d,if(dA019565(A304759(d)))); (m); };

A351032 a(n) = Product_{d|n, dA019565(A291759(d)).

Original entry on oeis.org

1, 1, 1, 2, 1, 2, 1, 4, 1, 2, 1, 24, 1, 6, 1, 8, 1, 12, 1, 8, 3, 6, 1, 480, 1, 2, 1, 72, 1, 120, 1, 16, 3, 2, 3, 480, 1, 2, 1, 32, 1, 216, 1, 120, 5, 6, 1, 13440, 3, 60, 1, 120, 1, 168, 3, 1440, 1, 6, 1, 144000, 1, 10, 3, 32, 1, 1080, 1, 8, 3, 72, 1, 26880, 1, 10, 75, 24, 9, 1080, 1, 128, 7, 10, 1, 86400, 1, 30, 3

Offset: 1

Antti Karttunen, Jan 29 2022

nonn

Index entries for sequences computed from indices in prime factorization

Cf. A019565, A048673, A289814, A291759, A351030, A351031, A351034 (rgs-transform).

Cf. also A293222.

A019565(n) = { my(m=1, p=1); while(n>0, p = nextprime(1+p); if(n%2, m *= p); n >>= 1); (m); };
A048673(n) = { my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); (1+factorback(f))/2; };
A289814(n) = { my(d=digits(n, 3)); fromdigits(vector(#d, i, if (d[i]==2, 1, 0)), 2); } \\ From A289814
A291759(n) = A289814(A048673(n));
A351032(n) = { my(m=1); fordiv(n,d,if(dA019565(A291759(d)))); (m); };

A351033 Lexicographically earliest infinite sequence such that a(i) = a(j) => A351031(i) = A351031(j), for all i, j >= 1.

Original entry on oeis.org

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

Offset: 1

Antti Karttunen, Jan 29 2022

Restricted growth sequence transform of A351031.

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

Cf. A019565, A048673, A289813, A304759, A351030, A351031, A351034.

Cf. also A293223.

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; };
A019565(n) = { my(m=1, p=1); while(n>0, p = nextprime(1+p); if(n%2, m *= p); n >>= 1); (m); };
A048673(n) = { my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); (1+factorback(f))/2; };
A289813(n) = { my(d=digits(n, 3)); fromdigits(vector(#d, i, if (d[i]==1, 1, 0)), 2); } \\ From A289813
A304759(n) = A289813(A048673(n));
A351031(n) = { my(m=1); fordiv(n,d,if(dA019565(A304759(d)))); (m); };
v351033 = rgs_transform(vector(up_to, n, A351031(n)));
A351033(n) = v351033[n];

A351034 Lexicographically earliest infinite sequence such that a(i) = a(j) => A351032(i) = A351032(j), for all i, j >= 1.

Original entry on oeis.org

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

Offset: 1

Antti Karttunen, Jan 29 2022

nonn

Restricted growth sequence transform of A351032.

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

Cf. A019565, A048673, A289814, A291759, A351030, A351032, A351033.

Cf. also A293224.

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; };
A019565(n) = { my(m=1, p=1); while(n>0, p = nextprime(1+p); if(n%2, m *= p); n >>= 1); (m); };
A048673(n) = { my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); (1+factorback(f))/2; };
A289814(n) = { my(d=digits(n, 3)); fromdigits(vector(#d, i, if (d[i]==2, 1, 0)), 2); } \\ From A289814
A291759(n) = A289814(A048673(n));
A351032(n) = { my(m=1); fordiv(n,d,if(dA019565(A291759(d)))); (m); };
v351034 = rgs_transform(vector(up_to, n, A351032(n)));
A351034(n) = v351034[n];

cp's OEIS Frontend

A351090 Lexicographically earliest infinite sequence such that a(i) = a(j) => A351091(i) = A351091(j) and A351092(i) = A351092(j), for all i, j >= 1.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

PARI

A351031 a(n) = Product_{d|n, dA019565(A304759(d)).

Views

Author

Keywords

Links

Crossrefs

Programs

PARI

A351032 a(n) = Product_{d|n, dA019565(A291759(d)).

Views

Author

Keywords

Links

Crossrefs

Programs

PARI

A351033 Lexicographically earliest infinite sequence such that a(i) = a(j) => A351031(i) = A351031(j), for all i, j >= 1.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

PARI

A351034 Lexicographically earliest infinite sequence such that a(i) = a(j) => A351032(i) = A351032(j), for all i, j >= 1.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

PARI