cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-4 of 4 results.

A329350 a(n) = Product_{d|n} A276086(d)^A010051(n/d).

Original entry on oeis.org

1, 2, 2, 3, 2, 18, 2, 9, 6, 54, 2, 45, 2, 30, 108, 15, 2, 150, 2, 405, 60, 270, 2, 375, 18, 150, 30, 675, 2, 33750, 2, 225, 540, 1350, 180, 3125, 2, 750, 300, 5625, 2, 281250, 2, 10125, 4500, 6750, 2, 140625, 10, 56250, 2700, 16875, 2, 468750, 1620, 84375, 1500, 33750, 2, 65625, 2, 42, 22500, 21, 900, 236250, 2, 567, 13500, 425250, 2, 21875
Offset: 1

Views

Author

Antti Karttunen, Nov 12 2019

Keywords

Links

Crossrefs

Cf. A010051, A069359, A276085, A276086, A329351 (rgs-transform).
Cf. also A329352, A329380.

Programs

  • PARI
    A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
A329350(n) = { my(m=1); fordiv(n,d,if(isprime(n/d), m *= A276086(d))); (m); };

Formula

a(n) = Product_{d|n} A276086(d)^A010051(n/d).
A276085(a(n)) = A069359(n).

A329381 Lexicographically earliest infinite sequence such that a(i) = a(j) => A329380(i) = A329380(j) for all i, j.

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, 16, 31, 32, 2, 33, 34, 35, 36, 37, 2, 38, 39, 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, 61, 62, 63, 64, 2, 65, 66, 67, 68, 69, 70, 71, 2, 72, 73
Offset: 1

Views

Author

Antti Karttunen, Nov 12 2019

Keywords

Comments

Restricted growth sequence transform of A329380.
For all i, j:
A305800(i) = A305800(j) => a(i) = a(j),
a(i) = a(j) => A323599(i) = A323599(j).

Links

Crossrefs

Cf. A001221, A276086, A305800, A323599, A329380.
Cf. also A329351.

Programs

  • PARI
    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; };
A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
A329380(n) = { my(m=1); fordiv(n,d,m *= A276086(d)^omega(n/d)); (m); };
v329381 = rgs_transform(vector(up_to, n, A329380(n)));
A329381(n) = v329381[n];

A329353 Lexicographically earliest infinite sequence such that a(i) = a(j) => A329352(i) = A329352(j) for all i, j.

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, 12, 18, 19, 2, 20, 2, 21, 22, 23, 24, 25, 2, 26, 27, 28, 2, 29, 2, 30, 31, 32, 2, 33, 7, 34, 35, 25, 2, 36, 27, 37, 38, 39, 2, 40, 2, 41, 42, 43, 44, 45, 2, 46, 47, 48, 2, 49, 2, 50, 51, 52, 53, 54, 2, 55, 56, 57, 2, 58, 59, 60, 61, 62, 2, 63, 64, 65, 66, 67, 68, 69, 2, 70, 71, 72, 2, 73, 2, 49, 74
Offset: 1

Views

Author

Antti Karttunen, Nov 12 2019

Keywords

Comments

Restricted growth sequence transform of A329352.
For all i, j:
A305800(i) = A305800(j) => a(i) = a(j),
a(i) = a(j) => A069359(i) = A069359(j).

Links

Crossrefs

Cf. A010051, A019565, A069359, A305800, A329352.
Cf. also A329351.
Differs from A319682 for the first time at n=254, where a(254)=123, while A319682(254)=184.

Programs

  • PARI
    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(j,v); factorback(Mat(vector(if(n, #n=vecextract(binary(n), "-1..1")), j, [prime(j), n[j]])~))}; \\ From A019565
A329352(n) = { my(m=1); fordiv(n,d,if(isprime(n/d), m *= A019565(d))); (m); };
v329353 = rgs_transform(vector(up_to, n, A329352(n)));
A329353(n) = v329353[n];

A380460 Lexicographically earliest infinite sequence such that a(i) = a(j) => A380459(i) = A380459(j), for all i, j >= 1, where A380459(n) = Product_{d|n} A276086(d)^A349394(n/d).

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, 8, 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, 60, 61, 20, 62, 2, 63, 64, 65, 66, 67, 68, 69, 2, 70, 71
Offset: 1

Views

Author

Antti Karttunen, Jan 31 2025

Keywords

Comments

Restricted growth sequence transform of A380459.
For all i, j >= 1:
A305800(i) = A305800(j) => a(i) = a(j),
a(i) = a(j) => A003415(i) = A003415(j),
a(i) = a(j) => A380467(i) = A380467(j),
a(i) = a(j) => A380477(i) = A380477(j).

Links

Crossrefs

Cf. A276086, A349394, A380459.
Cf. A003415, A305800, A380467, A380477.
Cf. also A329351, A329381.

Programs

  • PARI
    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; };
A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
A349394(n) = { my(p=0, e); if((e=isprimepower(n, &p)), p^(e-1), 0); };
A380459(n) = { my(m=1); fordiv(n, d, m *= A276086(d)^A349394(n/d)); (m); };
v380460 = rgs_transform(vector(up_to, n, A380459(n)));
A380460(n) = v380460[n];
Showing 1-4 of 4 results.

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