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 11-14 of 14 results.

A357173 Positions of records in A357171, i.e., integers whose number of divisors whose decimal digits are in strictly increasing order sets a new record.

Original entry on oeis.org

1, 2, 4, 6, 12, 24, 36, 48, 72, 144, 336, 468, 504, 936, 1008, 1512, 2520, 3024, 5040, 6552, 7560, 13104, 19656, 39312, 78624, 98280, 196560, 393120, 668304, 1244880, 1670760, 1867320, 3341520, 3734640, 7469280, 22407840, 26142480, 31744440, 52284960, 63488880
Offset: 1

Views

Author

Bernard Schott, Sep 17 2022

Keywords

Comments

As A009993 is finite, this sequence is necessarily finite.
Corresponding records are 1, 2, 3, 4, 6, 8, 9, 10, 11, ...

Examples

			a(6) = 24 is in the sequence because A357171(24) = 8 is larger than any earlier value in A357171.

Crossrefs

Cf. A009993, A357171, A357172, A160218.
Similar sequences: A093036, A340548, A355595.

Programs

  • Mathematica
    s[n_] := DivisorSum[n, 1 &, Less @@ IntegerDigits[#] &]; seq = {}; sm = 0; Do[If[(sn = s[n]) > sm, sm = sn; AppendTo[seq, n]], {n, 1, 10^4}]; seq (* Amiram Eldar, Sep 17 2022 *)
  • PARI
    isok(d) = Set(d=digits(d)) == d; \\ A009993
f(n) = sumdiv(n, d, isok(d)); \\ A357171
lista(nn) = my(r=0, list = List()); for (k=1, nn, my(m=f(k)); if (m>r, listput(list, k); r = m);); Vec(list); \\ Michel Marcus, Sep 18 2022

Extensions

More terms from Amiram Eldar, Sep 17 2022

A340638 Integers whose number of divisors that are Zuckerman numbers sets a new record.

Original entry on oeis.org

1, 2, 4, 6, 12, 24, 72, 144, 360, 432, 1080, 2016, 2160, 6048, 8064, 15120, 24192, 48384, 88704, 120960, 241920, 266112, 532224, 1064448, 1862784, 2661120, 3725568, 5322240, 7451136, 10450944, 19160064, 20901888, 28740096, 38320128, 57480192, 99283968, 114960384
Offset: 1

Views

Author

Bernard Schott, Jan 14 2021

Keywords

Comments

A Zuckerman number is a number that is divisible by the product of its digits (A007602).
The terms in this sequence are not necessarily Zuckerman numbers. For example a(7) = 72 has product of digits = 14 and 72/14 = 36/7 = 5.142...
The first seven terms are the first seven terms of A087997, then A087997(8) = 66 while a(8) = 144.

Examples

			The 8 divisors of 24 are all Zuckerman numbers, and also, 24 is the smallest integer that has at least 8 divisors that are Zuckerman numbers, hence 24 is a term.

Links

Crossrefs

Cf. A007602, A335037, A337941.
Subsequence of A335038.
Similar for palindromes (A093036), repdigits (A340548), repunits (A340549), Niven numbers (A340637).

Programs

  • Mathematica
    zuckQ[n_] := (prod = Times @@ IntegerDigits[n]) > 0 && Divisible[n, prod]; s[n_] := DivisorSum[n, 1 &, zuckQ[#] &]; smax = 0; seq = {}; Do[s1 = s[n]; If[s1 > smax, smax = s1; AppendTo[seq, n]], {n, 1, 10^5}]; seq (* Amiram Eldar, Jan 14 2021 *)
  • PARI
    isokz(n) = iferr(!(n % vecprod(digits(n))), E, 0); \\ A007602
lista(nn) = {my(m=0); for (n=1, nn, my(x = sumdiv(n, d, isokz(d));); if (x > m, m = x; print1(n, ", ")););} \\ Michel Marcus, Jan 15 2021

Extensions

More terms from David A. Corneth and Amiram Eldar, Jan 15 2021

A358101 Positions of records in A358099, i.e., integers whose number of divisors whose decimal digits are in strictly decreasing order sets a new record.

Original entry on oeis.org

1, 2, 4, 6, 12, 20, 30, 40, 60, 120, 240, 360, 420, 840, 1260, 2520, 5040, 8640, 10080, 15120, 20160, 30240, 60480, 120960, 181440, 362880, 544320, 786240, 1572480, 1874880, 3749760, 5624640, 7862400, 14938560, 23587200, 24373440, 31872960, 63745920, 95618880
Offset: 1

Views

Author

Bernard Schott, Nov 03 2022

Keywords

Comments

As A009995 is finite, this sequence is necessarily finite.
Corresponding records are 1, 2, 3, 4, 5, 6, 7, 8, 10, 11, ...

Examples

			a(9) = 60 is in the sequence because A358099(60) = 10 is larger than any earlier value in A358099.

Crossrefs

Cf. A009995, A190219, A358099, A358100.
Similar sequences: A093036, A340548, A357173.

Programs

  • Mathematica
    f[n_] := DivisorSum[n, 1 &, Greater @@ IntegerDigits[#] &]; fm = 0; s = {}; Do[If[(fn = f[n]) > fm, fm = fn; AppendTo[s, n]], {n, 1, 10^6}]; s (* Amiram Eldar, Nov 03 2022 *)

Extensions

More terms from Amiram Eldar, Nov 03 2022

A356179 Positions of records in A279497, i.e., integers whose number of pentagonal divisors sets a new record.

Original entry on oeis.org

1, 5, 35, 70, 210, 420, 2310, 4620, 18480, 32340, 60060, 120120, 240240, 720720, 1141140, 2042040, 4084080, 4564560, 13693680, 19399380, 38798760, 77597520, 232792560, 387987600
Offset: 1

Views

Author

Bernard Schott, Jul 28 2022

Keywords

Comments

The first fourteen terms are the same as A356132; then a(15) = 1141140 while A356132(15) = 1261260.
Corresponding records of number of pentagonal divisors are 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 16, ...

Examples

			210 is in the sequence because A279497(210) = 5 is larger than any earlier value in A279497.

Crossrefs

Cf. A000326, A279497, A356132.
Similar sequences: A046952, A093036, A350756, A355595.

Programs

  • Mathematica
    f[n_] := DivisorSum[n, 1 &, IntegerQ[(1 + Sqrt[1 + 24*#])/6] &]; fm = -1; s = {}; Do[If[(fn = f[n]) > fm, fm = fn; AppendTo[s, n]], {n, 1, 10^5}]; s (* Amiram Eldar, Jul 28 2022 *)
  • PARI
    lista(nn) = my(m=0); for (n=1, nn, my(new = sumdiv(n, d, ispolygonal(d, 5))); if (new > m, m = new; print1(n, ", "));); \\ Michel Marcus, Jul 28 2022

Extensions

a(23)-a(24) from David A. Corneth, Jul 28 2022
Previous Showing 11-14 of 14 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.