A344025 -id:A344025 - cp's OEIS frontend

A351236 Lexicographically earliest infinite sequence such that a(i) = a(j) => A344025(i) = A344025(j) and A351085(i) = A351085(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, 25, 26, 2, 27, 28, 29, 2, 30, 2, 31, 32, 33, 2, 34, 35, 36, 37, 38, 2, 39, 28, 40, 41, 21, 2, 42, 2, 43, 44, 45, 46, 47, 2, 48, 49, 50, 2, 51, 2, 52, 53, 54, 46, 55, 2, 56, 57, 58, 2, 59, 41, 60, 61, 62, 2, 63, 64, 65

Offset: 1

Antti Karttunen, Feb 06 2022

Restricted growth sequence transform of the 4-tuple [A003415(n), A003557(n), A327858(n), A345000(n)].

Question: If an image-analysis algorithm were to classify the scatter plot of this sequence, where it would cluster it? Nearer to A344025 than to A351085?

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

Cf. A003415, A003557, A327858, A345000, A351085.
Differs from A344025 for the first time at n=91, where a(91) = 64, while A344025(91) = 37.
Cf. also A305800, A351235, A351260.

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; };
A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A003557(n) = (n/factorback(factorint(n)[, 1]));
A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
A327858(n) = gcd(A003415(n),A276086(n));
A345000(n) = gcd(A003415(n),A003415(A276086(n)));
Aux351236(n) = [A003415(n), A003557(n), A327858(n), A345000(n)];
v351236 = rgs_transform(vector(up_to, n, Aux351236(n)));
A351236(n) = v351236[n];

A369051 Lexicographically earliest infinite sequence such that a(i) = a(j) => A003415(i) = A003415(j) and A085731(i) = A085731(j), for all i, j >= 1.

Original entry on oeis.org

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, 25, 26, 2, 27, 28, 29, 2, 30, 2, 31, 32, 33, 2, 34, 35, 36, 37, 38, 2, 39, 28, 40, 41, 21, 2, 40, 2, 42, 43, 44, 45, 46, 2, 47, 48, 49, 2, 50, 2, 51, 52, 53, 45, 54, 2, 55, 56, 57, 2, 58, 41, 59, 60, 61, 2, 62, 37

Offset: 1

Antti Karttunen, Jan 15 2024

nonn

Restricted growth sequence transform of the ordered pair [A003415(n), A085731(n)], or equally, of the pair [A003415(n), A083345(n)], or equally, of the pair [A083345(n), A085731(n)].

For all i, j: A369050(i) = A369050(j) => A344025(i) = A344025(j) => a(i) = a(j).

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

Cf. A003415, A083345, A085731.

Cf. also A344025, A369050.

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; };
A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A085731(n) = gcd(A003415(n),n);
Aux369051(n) = [A003415(n), A085731(n)];
v369051 = rgs_transform(vector(up_to, n, Aux369051(n)));
A369051(n) = v369051[n];

A351260 Lexicographically earliest infinite sequence such that a(i) = a(j) => A003415(i) = A003415(j), A003557(i) = A003557(j) and A046523(i) = A046523(j), for all i, j >= 1.

Original entry on oeis.org

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, 25, 26, 2, 27, 28, 29, 2, 30, 2, 31, 32, 33, 2, 34, 35, 36, 37, 38, 2, 39, 28, 40, 41, 42, 2, 43, 2, 44, 45, 46, 47, 48, 2, 49, 50, 51, 2, 52, 2, 53, 54, 55, 47, 56, 2, 57, 58, 59, 2, 60, 41, 61, 62, 63, 2, 64, 37, 65, 66, 67, 68, 69, 2, 70, 71, 72, 2, 73, 2, 74, 56

Offset: 1

Antti Karttunen, Feb 06 2022

Restricted growth sequence transform of the triplet [A003415(n), A003557(n), A046523(n)].
For all i, j >= 1:
  A305800(i) = A305800(j) => a(i) = a(j),
  a(i) = a(j) => A294877(i) = A294877(j),
  a(i) = a(j) => A300249(i) = A300249(j),
  a(i) = a(j) => A344025(i) = A344025(j).

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

Cf. A003415, A003557, A046523.
Cf. also A305800, A294877, A300249, A344025.
Differs from A300235, A305895 and A327931 for the first time at n=105, where a(105) = 56, while A300235(105) = A305895(105) = A327931(105) = 75.
Differs from A300249 for the first time at n=425, where a(425) = 299, while A300249(425) = 198.

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; };
A003415(n) = {my(fac); if(n<1, 0, fac=factor(n); sum(i=1, matsize(fac)[1], n*fac[i, 2]/fac[i, 1]))}; \\ From A003415
A003557(n) = (n/factorback(factorint(n)[, 1]));
A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };  \\ From A046523
Aux351260(n) = [A003415(n), A003557(n), A046523(n)];
v351260 = rgs_transform(vector(up_to,n,Aux351260(n)));
A351260(n) = v351260[n];

A353520 Lexicographically earliest infinite sequence such that a(i) = a(j) => A003415(i) = A003415(j), A003557(i) = A003557(j) and A053669(i) = A053669(j), for all i, j >= 1.

Original entry on oeis.org

1, 2, 3, 4, 3, 5, 3, 6, 7, 8, 3, 9, 3, 10, 11, 12, 3, 13, 3, 14, 15, 16, 3, 17, 18, 19, 20, 21, 3, 22, 3, 23, 24, 25, 26, 27, 3, 28, 29, 30, 3, 31, 3, 32, 33, 34, 3, 35, 36, 37, 38, 39, 3, 40, 29, 41, 42, 43, 3, 44, 3, 45, 46, 47, 48, 49, 3, 50, 51, 52, 3, 53, 3, 54, 55, 56, 48, 57, 3, 58, 59, 60, 3, 61, 42, 62, 63, 64, 3, 65, 38

Offset: 1

Antti Karttunen, Apr 25 2022

nonn

Restricted growth sequence transform of the triplet [A003415(n), A003557(n), A053669(n)].
For all i, j:
  A305801(i) = A305801(j) => a(i) = a(j),
  a(i) = a(j) => A007814(i) = A007814(j),
  a(i) = a(j) => A344025(i) = A344025(j).

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

Cf. A003415, A003557, A007814, A053669.

Cf. also A305801, A328470, A344025, A351260.

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; };
A003415(n) = {my(fac); if(n<1, 0, fac=factor(n); sum(i=1, matsize(fac)[1], n*fac[i, 2]/fac[i, 1]))}; \\ From A003415
A003557(n) = (n/factorback(factorint(n)[, 1]));
A053669(n) = forprime(p=2, , if(n%p, return(p))); \\ From A053669
Aux353520(n) = [A003415(n), A003557(n), A053669(n)];
v353520 = rgs_transform(vector(up_to,n,Aux353520(n)));
A353520(n) = v353520[n];

A369050 Lexicographically earliest infinite sequence such that a(i) = a(j) => f(i) = f(j), where f(1) = 1, and for n>1, f(n) = [A003415(n), A369049(n)], for all i, j >= 1.

Original entry on oeis.org

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, 25, 26, 2, 27, 28, 29, 2, 30, 2, 31, 32, 33, 2, 34, 35, 36, 37, 38, 2, 39, 28, 40, 41, 42, 2, 43, 2, 44, 45, 46, 47, 48, 2, 49, 50, 51, 2, 52, 2, 53, 54, 55, 56, 57, 2, 58, 59, 60, 2, 61, 62, 63, 64, 65, 2, 66, 37

Offset: 1

Antti Karttunen, Jan 15 2024

nonn

Restricted growth sequence transform of the function f defined as: f(1) = 1, and for n>1, f(n) = [A003415(n), A369049(n)].
For all i, j:
  A305800(i) = A305800(j) => a(i) = a(j),
  a(i) = a(j) => A344025(i) = A344025(j) => A369051(i) = A369051(j).

Antti Karttunen, Table of n, a(n) for n = 1..100000

Cf. A003415, A369049.
Cf. also A305800, A328767, A344025, A369051.
Differs from A351260 for the first time at n=77, where a(77) = 56, while A351260(77) = 47.
Differs from A300833 for the first time at n=91, where a(91) = 37, while A300833(91) = 67.

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; };
A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A369049(n) = (n % A003415(n));
Aux369050(n) = if(1==n,1,[A003415(n), A369049(n)]);
v369050 = rgs_transform(vector(up_to, n, Aux369050(n)));
A369050(n) = v369050[n];

A353521 Lexicographically earliest infinite sequence such that a(i) = a(j) => A003415(i) = A003415(j), A003557(i) = A003557(j) and A000035(i) = A000035(j), for all i, j >= 1.

Original entry on oeis.org

1, 2, 3, 4, 3, 5, 3, 6, 7, 8, 3, 9, 3, 10, 11, 12, 3, 13, 3, 14, 15, 16, 3, 17, 18, 19, 20, 21, 3, 22, 3, 23, 24, 25, 26, 27, 3, 28, 29, 30, 3, 31, 3, 32, 33, 34, 3, 35, 36, 37, 38, 39, 3, 40, 29, 41, 42, 22, 3, 43, 3, 44, 45, 46, 47, 48, 3, 49, 50, 51, 3, 52, 3, 53, 54, 55, 47, 56, 3, 57, 58, 59, 3, 60, 42, 61, 62, 63, 3, 64, 38

Offset: 1

Antti Karttunen, Apr 27 2022

nonn

Restricted growth sequence transform of the triplet [A003415(n), A003557(n), A000035(n)].
For all i, j:
  A305801(i) = A305801(j) => A353520(i) = A353520(j) => a(i) = a(j),
  a(i) = a(j) => A007814(i) = A007814(j),
  a(i) = a(j) => A344025(i) = A344025(j),
  a(i) = a(j) => A353522(i) = A353522(j).

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

Cf. A000035, A003415, A003557, A007814.

Cf. also A305801, A344025, A351260, A353520, A353522.

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; };
A000035(n) = (n%2);
A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A003557(n) = (n/factorback(factorint(n)[, 1]));
Aux353521(n) = [A003415(n), A003557(n), A000035(n)];
v353521 = rgs_transform(vector(up_to,n,Aux353521(n)));
A353521(n) = v353521[n];

A353523 Lexicographically earliest infinite sequence such that a(i) = a(j) => A349905(i) = A349905(j) and A003557(i) = A003557(j), for all i, j >= 1.

Original entry on oeis.org

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

Offset: 1

Antti Karttunen, Apr 27 2022

nonn

Restricted growth sequence transform of the ordered pair [A003557(n), A349905(n)], or equally, of the ordered pair [A003415(A003961(n)), A003557(A003961(n))].
This is a prime-shifted variant of A344025, as this is the restricted growth sequence transform of A344025(A003961(n)).
For all i, j:
  A305800(i) = A305800(j) => a(i) = a(j),
  a(i) = a(j) => A349905(i) = A349905(j) => A008836(i) = A008836(j),
  a(i) = a(j) => A353571(i) = A353571(j).

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

Cf. A003415, A003557, A003961, A008836, A305800, A344025, A349905, A353571.

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; };
A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A003557(n) = (n/factorback(factorint(n)[, 1]));
A003961(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); }; \\ From A003961
Aux353523(n) = { my(s=A003961(n)); [A003415(s), A003557(s)]; };
v353523 = rgs_transform(vector(up_to, n, Aux353523(n)));
A353523(n) = v353523[n];

A369046 Lexicographically earliest infinite sequence such that a(i) = a(j) => A003415(i) = A003415(j) and A069359(i) = A069359(j), for all i, j >= 1.

Original entry on oeis.org

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, 25, 26, 2, 27, 28, 29, 2, 30, 2, 31, 32, 33, 2, 34, 35, 36, 37, 38, 2, 39, 28, 40, 41, 21, 2, 42, 2, 43, 44, 45, 46, 47, 2, 48, 49, 50, 2, 51, 2, 52, 53, 54, 46, 55, 2, 56, 57, 58, 2, 59, 41, 60, 61, 62, 2, 63, 37

Offset: 1

Antti Karttunen, Jan 18 2024

nonn

Restricted growth sequence transform of the ordered pair [A003415(n), A069359(n)].
For all i,j >= 1:
  A369050(i) = A369050(j) => a(i) = a(j), [Conjectured]
  a(i) = a(j) => A329039(i) = A329039(j) => A008966(i) = A008966(j).

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

Cf. A003415, A008966, A069359, A329039.
Cf. also A369050, A369051.
Differs from A351236 for the first time at n=91, where a(91) = 37, while A351236(91) = 64.
Differs from A344025 for the first time at n=140, where a(140) = 97, while A344025(140) = 92.

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; };
A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A069359(n) = (n*sumdiv(n, d, isprime(d)/d));
Aux369046(n) = [A003415(n), A069359(n)];
v369046 = rgs_transform(vector(up_to, n, Aux369046(n)));
A369046(n) = v369046[n];

A373268 Lexicographically earliest infinite sequence such that a(i) = a(j) => A003415(i) = A003415(j), A085731(i) = A085731(j) and A373145(i) = A373145(j), for all i, j >= 1.

Original entry on oeis.org

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, 25, 26, 2, 27, 28, 29, 2, 30, 2, 31, 32, 33, 2, 34, 35, 36, 37, 38, 2, 39, 28, 40, 41, 21, 2, 42, 2, 43, 44, 45, 46, 47, 2, 48, 49, 50, 2, 51, 2, 52, 53, 54, 46, 55, 2, 56, 57, 58, 2, 59, 41, 60, 61, 62, 2, 63, 64, 65, 66, 67, 68, 69, 2, 70, 71, 72, 2, 73, 2, 74, 55

Offset: 1

Antti Karttunen, Jun 09 2024

nonn

Restricted growth sequence transform of the triple [A003415(n), A085731(n), A373145(n)].
For all i, j >= 1:
  A373150(i) = A373150(j) => a(i) = a(j),
  a(i) = a(j) => A373151(i) = A373151(j) => A373485(i) = A373485(j),
  a(i) = a(j) => A373152(i) = A373152(j),
  a(i) = a(j) => A373486(i) = A373486(j).

Antti Karttunen, Table of n, a(n) for n = 1..100000

Cf. A003415, A083345, A085731, A276085, A373145.
Cf. A373150, A373151, A373152, A373485, A373486.
Differs from A344025 and A369046 for the first time at n=91, where a(91) = 64, while A344025(91) = A369046(91) = 37.
Differs from A351236 for the first time at n=143, where a(143) = 100, while A351236(143) = 68.

up_to = 100000;
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; };
A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A276085(n) = { my(f = factor(n)); sum(k=1, #f~, f[k, 2]*prod(i=1,primepi(f[k, 1]-1),prime(i))); };
Aux373268(n) = { my(d=A003415(n)); [d, gcd(d,n), gcd(d, A276085(n))]; };
v373268 = rgs_transform(vector(up_to, n, Aux373268(n)));
A373268(n) = v373268[n];

A379240 Lexicographically earliest infinite sequence such that a(i) = a(j) => f(i) = f(j), for all i, j, where f(n) = [A003415(n), A085731(n)] if A359550(n) = 1, otherwise f(n) = n.

Original entry on oeis.org

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, 25, 26, 2, 27, 28, 29, 2, 30, 2, 31, 32, 33, 2, 34, 35, 36, 37, 38, 2, 39, 28, 40, 41, 21, 2, 42, 2, 43, 44, 45, 46, 47, 2, 48, 49, 50, 2, 51, 2, 52, 53, 54, 46, 55, 2, 56, 57, 58, 2, 59, 41, 60, 61, 62, 2, 63, 37, 64

Offset: 1

Antti Karttunen, Dec 19 2024

nonn

It is conjectured that this is also the lexicographically earliest infinite sequence such that a(i) = a(j) => A003415(i) = A003415(j), A085731(i) = A085731(j) and A376418(i) = A376418(j), for all i, j >= 1, i.e., the restricted growth sequence transform of the triple [A003415(n), A085731(n), A376418(n)]. This is true if for every pair of i and j for which i <> j, and A376418(i) = A376418(j) > 0, the ordered pairs [A003415(i), A085731(i)] and [A003415(j), A085731(j)] differ from each other.

Antti Karttunen, Table of n, a(n) for n = 1..100000

Cf. A003415, A048103, A083345, A085371, A100716, A359550, A369051, A376418.
Differs from A344025 first at n=140, where a(140) = 97, while A344025(140) = 92.
Differs from A369046 first at n=171, where a(171) = 63, while A369046(171) = 121.

up_to = 100000;
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; };
A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A359550(n) = { my(pp); forprime(p=2, , pp = p^p; if(!(n%pp), return(0)); if(pp > n, return(1))); };
Aux379240(n) = if(!A359550(n), n, my(d=A003415(n)); [d, gcd(d,n)]);
v379240 = rgs_transform(vector(up_to, n, Aux379240(n)));
A379240(n) = v379240[n];

For all i, j >= 1:
  a(i) = a(j) => A369051(i) = A369051(j) => A083345(i) = A083345(j),
  a(i) = a(j) => A376418(i) = A376418(j).

cp's OEIS Frontend

A351236 Lexicographically earliest infinite sequence such that a(i) = a(j) => A344025(i) = A344025(j) and A351085(i) = A351085(j) for all i, j >= 1.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

PARI

A369051 Lexicographically earliest infinite sequence such that a(i) = a(j) => A003415(i) = A003415(j) and A085731(i) = A085731(j), for all i, j >= 1.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

PARI

A351260 Lexicographically earliest infinite sequence such that a(i) = a(j) => A003415(i) = A003415(j), A003557(i) = A003557(j) and A046523(i) = A046523(j), for all i, j >= 1.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

PARI

A353520 Lexicographically earliest infinite sequence such that a(i) = a(j) => A003415(i) = A003415(j), A003557(i) = A003557(j) and A053669(i) = A053669(j), for all i, j >= 1.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

PARI

A369050 Lexicographically earliest infinite sequence such that a(i) = a(j) => f(i) = f(j), where f(1) = 1, and for n>1, f(n) = [A003415(n), A369049(n)], for all i, j >= 1.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

PARI

A353521 Lexicographically earliest infinite sequence such that a(i) = a(j) => A003415(i) = A003415(j), A003557(i) = A003557(j) and A000035(i) = A000035(j), for all i, j >= 1.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

PARI

A353523 Lexicographically earliest infinite sequence such that a(i) = a(j) => A349905(i) = A349905(j) and A003557(i) = A003557(j), for all i, j >= 1.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

PARI

A369046 Lexicographically earliest infinite sequence such that a(i) = a(j) => A003415(i) = A003415(j) and A069359(i) = A069359(j), for all i, j >= 1.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

PARI

A373268 Lexicographically earliest infinite sequence such that a(i) = a(j) => A003415(i) = A003415(j), A085731(i) = A085731(j) and A373145(i) = A373145(j), for all i, j >= 1.

Views

Author

Keywords

Comments

Links

Crossrefs