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.

Previous Showing 31-35 of 35 results.

A379006 Ordinal transform of A355582, where A355582 is the largest 5-smooth divisor of n.

Original entry on oeis.org

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

Views

Author

Antti Karttunen, Dec 15 2024

Keywords

Links

Crossrefs

Cf. A355582.
Cf. A379005 (ordinal transform).
Cf. also A003602, A126760.

Programs

  • PARI
    up_to = 20000;
ordinal_transform(invec) = { my(om = Map(), outvec = vector(length(invec)), pt); for(i=1, length(invec), if(mapisdefined(om,invec[i]), pt = mapget(om, invec[i]), pt = 0); outvec[i] = (1+pt); mapput(om,invec[i],(1+pt))); outvec; };
is_A051037(n) = (n<7||vecmax(factor(n, 6)[, 1])<7); \\ From A051037
A355582(n) = fordiv(n,d,if(is_A051037(n/d),return(n/d)));
v379006 = ordinal_transform(vector(up_to, n, A355582(n)));
A379006(n) = v379006[n];

A322317 Ordinal transform of A322316.

Original entry on oeis.org

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

Views

Author

Antti Karttunen, Dec 04 2018

Keywords

Links

Crossrefs

Cf. A007814, A007949, A122841, A244417, A322316.
Cf. also A126760.

Programs

  • PARI
    up_to = 65537;
ordinal_transform(invec) = { my(om = Map(), outvec = vector(length(invec)), pt); for(i=1, length(invec), if(mapisdefined(om,invec[i]), pt = mapget(om, invec[i]), pt = 0); outvec[i] = (1+pt); mapput(om,invec[i],(1+pt))); outvec; };
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; };
A007814(n) = valuation(n,2);
A007949(n) = valuation(n,3);
A122841(n) = min(A007814(n), A007949(n));
A244417(n) = max(valuation(n,2), valuation(n,3));
v322316 = rgs_transform(vector(up_to, n, [A122841(n), A244417(n)]));
v322317 = ordinal_transform(v322316);
A322317(n) = v322317[n];

A353335 Dirichlet inverse of A353420.

Original entry on oeis.org

1, -1, -2, 0, -3, 2, -4, 0, -5, 3, -5, 0, -6, 4, 0, 0, -7, 5, -8, 0, -3, 5, -10, 0, -8, 6, -14, 0, -11, 0, -13, 0, -2, 7, -2, 0, -14, 8, -5, 0, -15, 3, -16, 0, 7, 10, -18, 0, -25, 8, -4, 0, -20, 14, -1, 0, -7, 11, -21, 0, -23, 13, 8, 0, -4, 2, -24, 0, -9, 2, -25, 0, -27, 14, 4, 0, -8, 5, -28, 0, -52, 15, -30, 0, -3
Offset: 1

Views

Author

Antti Karttunen, Apr 20 2022

Keywords

Links

Crossrefs

Cf. A003961, A126760, A353420, A353336.

Programs

  • PARI
    up_to = 65537;
DirInverseCorrect(v) = { my(u=vector(#v)); u[1] = (1/v[1]); for(n=2, #v, u[n] = (-u[1]*sumdiv(n, d, if(dA003961(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
A126760(n) = {n&&n\=3^valuation(n, 3)<A126760
A353420(n) = A126760(A003961(n));
v353335 = DirInverseCorrect(vector(up_to,n,A353420(n)));
A353335(n) = v353335[n];

Formula

a(1) = 1; a(n) = -Sum_{d|n, d < n} A353420(n/d) * a(d).
a(n) = A353336(n) - A353420(n).

A379003 Ordinal transform of A132741, where A132741 is the largest divisor of n having the form 2^i*5^j. a(0) = 0 by convention.

Original entry on oeis.org

0, 1, 1, 2, 1, 1, 2, 3, 1, 4, 1, 5, 2, 6, 3, 2, 1, 7, 4, 8, 1, 9, 5, 10, 2, 1, 6, 11, 3, 12, 2, 13, 1, 14, 7, 3, 4, 15, 8, 16, 1, 17, 9, 18, 5, 4, 10, 19, 2, 20, 1, 21, 6, 22, 11, 5, 3, 23, 12, 24, 2, 25, 13, 26, 1, 6, 14, 27, 7, 28, 3, 29, 4, 30, 15, 2, 8, 31, 16, 32, 1, 33, 17, 34, 9, 7, 18, 35, 5, 36, 4, 37, 10
Offset: 0

Views

Author

Antti Karttunen, Dec 15 2024

Keywords

Comments

Ordinal transform of the ordered pair [A007814(n), A112765(n)].
This sequence and A379004 are ordinal transforms of each other (if the initial 0 is discarded).

Links

Crossrefs

Cf. A007814, A112765, A132741, A379004 (ordinal transform of this sequence after the initial 0).
Cf. also A126760, A379006.

Programs

  • PARI
    up_to = 20000;
ordinal_transform(invec) = { my(om = Map(), outvec = vector(length(invec)), pt); for(i=1, length(invec), if(mapisdefined(om,invec[i]), pt = mapget(om, invec[i]), pt = 0); outvec[i] = (1+pt); mapput(om,invec[i],(1+pt))); outvec; };
v379003 = ordinal_transform(vector(up_to, n, [valuation(n,2), valuation(n,5)]));
A379003(n) = if(!n,n,v379003[n]);

A353278 Ordinal transform of the function f(n) = [A020639(n), A341353(n)] for n > 1, with f(1) = 1.

Original entry on oeis.org

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

Views

Author

Antti Karttunen, Apr 10 2022

Keywords

Comments

Also the ordinal transform of A353277.

Links

Crossrefs

Cf. A007814, A007949, A020639, A156552, A341353, A353277.
Cf. also A078898, A126760.

Programs

  • PARI
    up_to = 65537;
ordinal_transform(invec) = { my(om = Map(), outvec = vector(length(invec)), pt); for(i=1, length(invec), if(mapisdefined(om,invec[i]), pt = mapget(om, invec[i]), pt = 0); outvec[i] = (1+pt); mapput(om,invec[i],(1+pt))); outvec; };
A007814(n) = valuation(n,2);
A007949(n) = valuation(n,3);
A156552(n) = { my(f = factor(n), p, p2 = 1, res = 0); for(i = 1, #f~, p = 1 << (primepi(f[i, 1]) - 1); res += (p * p2 * (2^(f[i, 2]) - 1)); p2 <<= f[i, 2]); res };
Aux353278(n) = if(1==n,1,my(u=A156552(n)); [A007814(u), A007949(u)]);
v353278 = ordinal_transform(vector(up_to, n, Aux353278(n)));
A353278(n) = v353278[n];
Previous Showing 31-35 of 35 results.

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