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 1-3 of 3 results.

A328626 Inverse permutation to A328625.

Original entry on oeis.org

0, 1, 2, 5, 4, 3, 6, 7, 20, 17, 16, 21, 12, 13, 8, 29, 28, 9, 18, 19, 26, 11, 10, 27, 24, 25, 14, 23, 22, 15, 30, 31, 32, 35, 34, 33, 126, 127, 80, 167, 166, 81, 162, 163, 128, 119, 118, 129, 78, 79, 116, 131, 130, 117, 114, 115, 164, 83, 82, 165, 60, 61, 62, 65, 64, 63, 36, 37, 140, 107, 106, 141, 102, 103, 38, 209, 208, 39, 138, 139, 206, 41, 40
Offset: 0

Views

Author

Antti Karttunen, Oct 25 2019

Keywords

Links

Crossrefs

Cf. A328625 (inverse permutation).
Cf. A049345, A276085, A328620, A328627, A328629.
Cf. also A289234, A328623.

Programs

  • PARI
    A002110(n) = prod(i=1,n,prime(i));
A276085(n) = { my(f = factor(n)); sum(k=1, #f~, f[k, 2]*A002110(primepi(f[k, 1])-1)); };
A328627(n) = { my(m=1, p=2, d=0); while(n, d = lift(Mod(n,p)/(d+1)); m *= (p^d); n = n\p; p = nextprime(1+p)); (m); };
A328626(n) = A276085(A328627(n));

Formula

a(n) = A276085(A328627(n)).
For all n, A328620(a(n)) = A328620(n).

A328627 Twisted variant of A276086 indexed by A328626.

Original entry on oeis.org

1, 2, 3, 18, 9, 6, 5, 10, 375, 450, 225, 750, 25, 50, 15, 11250, 5625, 30, 125, 250, 1875, 90, 45, 3750, 625, 1250, 75, 2250, 1125, 150, 7, 14, 21, 126, 63, 42, 12005, 24010, 18375, 7563150, 3781575, 36750, 420175, 840350, 36015, 3858750, 1929375, 72030, 6125, 12250, 643125, 216090, 108045, 1286250, 214375, 428750
Offset: 0

Views

Author

Antti Karttunen, Oct 25 2019

Keywords

Links

Crossrefs

Cf. A276086, A328624, A328626, A328629.

Programs

  • PARI
    A328627(n) = { my(m=1, p=2, d=0); while(n, d = lift(Mod(n,p)/(d+1)); m *= (p^d); n = n\p; p = nextprime(1+p)); (m); };

Formula

a(n) = A276086(A328626(n)).

A328628 Lexicographically earliest infinite sequence such that a(i) = a(j) => A046523(A328624(i)) = A046523(A328624(j)) for all i, j.

Original entry on oeis.org

1, 2, 2, 3, 4, 5, 2, 5, 3, 6, 7, 8, 4, 3, 9, 10, 3, 11, 12, 13, 5, 14, 15, 16, 17, 9, 13, 18, 19, 14, 2, 5, 5, 14, 3, 11, 3, 14, 6, 20, 21, 22, 7, 18, 23, 24, 18, 25, 26, 23, 16, 27, 28, 29, 30, 31, 32, 33, 34, 35, 4, 3, 3, 6, 19, 14, 9, 16, 10, 36, 37, 38, 39, 40, 41, 42, 40, 43, 13, 8, 11, 44, 10, 45, 26, 23, 46, 47, 21, 22, 12, 13, 13, 18, 7, 8, 48, 49, 40
Offset: 0

Views

Author

Antti Karttunen, Oct 25 2019

Keywords

Comments

Restricted growth sequence transform of function f(n) = A046523(A328624(n)) = A278226(A328625(n)).
For all i, j:
a(i) = a(j) => A328630(i) = A328630(j).
The scatter plot looks like a mound (or hive) of insects. - Antti Karttunen, Jan 09 2023

Links

Crossrefs

Cf. A046523, A278226, A328624, A328625, A328629, A328630.

Programs

  • PARI
    up_to = 32768;
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; };
A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); }; \\ From A046523
A328624(n) = { my(m=1, p=2, e, g=1); while(n, e = (n%p); m *= (p^((g*e)%p)); g = e+1; n = n\p; p = nextprime(1+p)); (m); };
Aux328628(n) = A046523(A328624(n));
v328628 = rgs_transform(vector(1+up_to, n, Aux328628(n-1)));
A328628(n) = v328628[1+n];
Showing 1-3 of 3 results.

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