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.

A279541 Indices of records in A192013: Sum_{d|n} Kronecker(-6, d).

Original entry on oeis.org

1, 5, 25, 35, 175, 385, 1225, 1925, 9625, 13475, 48125, 55825, 148225, 279125, 390775, 1395625, 1730575, 4298525, 8652875, 12114025, 43264375, 60570125, 133254275, 302850625, 423990875, 642043325, 2119954375
Offset: 1

Views

Author

Charles R Greathouse IV, Dec 14 2016

Keywords

Links

Crossrefs

Cf. A192013, A279542, A109017.

Programs

  • PARI
    smooth(P:vec, lim)=my(v=List([1]), nxt=vector(#P, i, 1), indx, t); while(1, t=vecmin(vector(#P, i, v[nxt[i]]*P[i]), &indx); if(t>lim, break); if(t>v[#v], listput(v, t)); nxt[indx]++); Vec(v);
ok(p)=p=p%24; p==1 || p==5 || p==7 || p==11;
A192013(n)=sumdivmult(n, d, kronecker(-6, d));
list(lim)=my(u=List([1]),v=[5],r,t); forprime(p=7,, if(ok(p), if(v[#v]*p>lim, break); v=concat(v, v[#v]*p))); v=smooth(v,lim); for(i=2,#v, t=A192013(v[i]); if(t>r, r=t; listput(u,v[i]))); Vec(u)

A344472 Record values in A002324.

Original entry on oeis.org

1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 64, 72, 96, 108, 128, 144, 160, 192, 216, 256, 288, 320, 384, 432, 512, 576, 640, 768, 864, 1024, 1152, 1280, 1536, 1728, 2048, 2304, 2560, 3072, 3456, 3840, 4096, 4608, 5120, 5184, 6144, 6912, 7680, 8192, 9216
Offset: 1

Views

Author

Jianing Song, May 20 2021

Keywords

Comments

Also numbers k such that A343771(m) > A343771(k) for all m > k.

Examples

			8 is a term because the circle with radius sqrt(1729) centered at the origin hits exactly 6*8 = 48 points in the A_2 lattice, and any circle with radius < sqrt(1729) centered at the origin hits fewer than 48 points.

Links

Crossrefs

Cf. A230655, A344471, A002324, A343771, A000005, A344473.
Records of Sum_{d|n} kronecker(m, d): this sequence (m=-3), A344470 (m=-4), A279542 (m=-6).

Programs

  • PARI
    my(v=list_A344473(10^15), rec=0); for(n=1, #v, if(numdiv(v[n])>rec, rec=numdiv(v[n]); print1(rec, ", "))) \\ see program for A344473

Formula

a(n) = A344471(n+1)/6.
a(n) = A000005(A230655(n+1)) = A002324(A230655(n+1)).

A344470 Record values in A002654.

Original entry on oeis.org

1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 20, 24, 32, 36, 40, 48, 64, 72, 80, 96, 128, 144, 160, 192, 216, 256, 288, 320, 384, 432, 512, 576, 640, 768, 864, 960, 1024, 1152, 1280, 1536, 1728, 1920, 2048, 2304, 2560, 2880, 3072, 3456, 3840, 4096, 4608, 5120, 5760, 6144
Offset: 1

Views

Author

Jianing Song, May 20 2021

Keywords

Comments

Also numbers k such that A018782(m) > A018782(k) for all m > k.

Examples

			9 is a term because the circle with radius sqrt(4225) centered at the origin hits exactly 4*9 = 36 integer points, and any circle with radius < sqrt(4225) centered at the origin hits fewer than 36 points.

Links

Crossrefs

Cf. A071383, A071385, A002654, A018782, A000005, A054994.
Records of Sum_{d|n} kronecker(m, d): A344472 (m=-3), this sequence (m=-4), A279542 (m=-6).

Programs

  • PARI
    my(v=list(10^15), rec=0); for(n=1, #v, if(numdiv(v[n])>rec, rec=numdiv(v[n]); print1(rec, ", "))) \\ see program for A054994

Formula

a(n) = A071385(n+1)/4.
a(n) = A000005(A071383(n+1)) = A002654(A071383(n+1)).
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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