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 1-2 of 2 results.

A382325 Numbers with a record ratio of proper factorizations to nontrivial divisors.

Original entry on oeis.org

4, 16, 32, 64, 128, 192, 256, 384, 512, 576, 768, 864, 1024, 1152, 1536, 1728, 2304, 3456, 4608, 5184, 5760, 6912, 8640, 9216, 10368, 11520, 13824, 17280, 20736, 23040, 25920, 27648, 34560, 41472, 51840, 62208, 69120, 82944, 103680, 138240, 165888, 172800
Offset: 1

Views

Author

Charles L. Hohn, Mar 21 2025

Keywords

Comments

Numbers k that give a record value for A028422(k)/A070824(k).
a(n) = 0 (mod 4), and with prime factors of terms clustering around the smallest primes, it is observed that as n increases, the gcd of a(n)..a(oo) remains among the largest divisors of a(n).

Examples

			a(1)=4: |{{2, 2}}| / |{2}| = 1/1.
a(2)=16: |{{2, 2, 2, 2}, {2, 2, 4}, {2, 8}, {4, 4}}| / |{2, 4, 8}| = 4/3.
a(3)=32: |{{2, 2, 2, 2, 2}, {2, 2, 2, 4}, {2, 2, 8}, {2, 4, 4}, {2, 16}, {4, 8}}| / |{2, 4, 8, 16}| = 6/4.

Crossrefs

Cf. A028422, A070824, A033833, A002182, A382326, A382327.
Subsequence of A025487.

Programs

  • PARI
    f_count(x, f=List())={my(r=x/if(#f, vecprod(Vec(f)), 1)); if(r==1, return(if(#f, 1, 0))); my(d, c=0); fordiv(r, d, if(d==1 || d==x || (#f && dmx, mx=m; print1(x, ", ")))

A382326 Numbers with a record ratio of nontrivial divisors to prime factors (counted with multiplicity).

Original entry on oeis.org

4, 6, 12, 24, 30, 60, 120, 180, 210, 360, 420, 840, 1260, 2310, 2520, 4620, 7560, 9240, 13860, 27720, 55440, 60060, 83160, 110880, 120120, 138600, 166320, 180180, 277200, 360360, 720720, 1081080, 1441440, 1801800, 2162160, 3063060, 3603600, 5405400, 6126120
Offset: 1

Views

Author

Charles L. Hohn, Mar 21 2025

Keywords

Comments

Numbers k that give a record value for A070824(k)/A001222(k).

Examples

			a(1) = 4: |{2}| / |{2, 2}| = 1/2.
a(2) = 6: |{2, 3}| / |{2, 3}| = 2/2.
a(3) = 12: |{2, 3, 4, 6}| / |{2, 2, 3}| = 4/3.

Crossrefs

Cf. A070824, A001222, A002182, A382325, A382327.
Subsequence of A025487.

Programs

  • PARI
    my(mx=0); for(x=2, 10^5, my(f=factor(x), m=(numdiv(f)-2)/bigomega(f)); if(m>mx, mx=m; print1(x, ", ")))
Showing 1-2 of 2 results.

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

Content is available under The OEIS End-User License Agreement.