A351032 -id:A351032 - cp's OEIS frontend

A351030 Lexicographically earliest infinite sequence such that a(i) = a(j) => A351031(i) = A351031(j) and A351032(i) = A351032(j), for all i, j >= 1.

1, 2, 2, 3, 2, 4, 2, 5, 6, 7, 2, 8, 2, 9, 10, 11, 2, 12, 2, 13, 14, 15, 2, 16, 17, 18, 19, 20, 2, 21, 2, 22, 23, 24, 23, 25, 2, 26, 27, 28, 2, 29, 2, 30, 31, 32, 2, 33, 34, 35, 36, 37, 2, 38, 39, 40, 41, 42, 2, 43, 2, 44, 45, 46, 36, 47, 2, 48, 49, 50, 2, 51, 2, 52, 53, 54, 55, 56, 2, 57, 58, 59, 2, 60, 61, 62

Offset: 1

Antti Karttunen, Jan 29 2022

nonn

Restricted growth sequence transform of the ordered pair [A351031(n), A351032(n)], or equally, of the ordered pair [A351033(n), A351034(n)].

For all i, j: a(i) = a(j) => A349910(i) = A349910(j).

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, A289814, A291759, A304759, A351031, A351032 A351033, A351034.

Cf. also A293226, A349910.

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); };
A289814(n) = { my(d=digits(n, 3)); fromdigits(vector(#d, i, if (d[i]==2, 1, 0)), 2); };
A291759(n) = A289814(A048673(n));
A304759(n) = A289813(A048673(n));
A351031(n) = { my(m=1); fordiv(n,d,if(dA019565(A304759(d)))); (m); };
A351032(n) = { my(m=1); fordiv(n,d,if(dA019565(A291759(d)))); (m); };
Aux351030(n) = [A351031(n),A351032(n)];
v351030 = rgs_transform(vector(up_to, n, Aux351030(n)));
A351030(n) = v351030[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];

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); };

cp's OEIS Frontend

A351030 Lexicographically earliest infinite sequence such that a(i) = a(j) => A351031(i) = A351031(j) and A351032(i) = A351032(j), for all i, j >= 1.

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

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

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