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 1-4 of 4 results.

A365263 Numbers m for which A139770(m) and A140635(m) differ.

Original entry on oeis.org

16, 64, 81, 144, 192, 320, 324, 400, 448, 576, 625, 704, 729, 784, 832, 900, 960, 1024, 1088, 1216, 1296, 1344, 1458, 1472, 1600, 1728, 1764, 1856, 1936, 1984, 2025, 2112, 2240, 2304, 2368, 2401, 2496, 2500, 2624, 2704, 2752, 2880, 2916, 3008, 3072, 3136, 3264, 3392, 3520, 3600, 3645, 3648, 3776, 3904, 3969
Offset: 1

Views

Author

Hartmut F. W. Hoft, Aug 29 2023

Keywords

Links

Crossrefs

Cf. A000005, A002182, A005179, A007412, A061799, A139770, A140635.

Programs

  • Mathematica
    (* a139770[ ] and a140635[ ] are defined in their respective sequences *)
a365263[{m_, n_}] := Select[Range[m, n], a139770[#]!=a140635[#]&]
a365263[{1, 4000}]
  • PARI
    isok(m) = my(nd = numdiv(m)); for (i=1, m-1, if (numdiv(i) == nd, return (0)); if (numdiv(i)> nd, return(1))); 0; \\ Michel Marcus, Aug 31 2023

A140635 Smallest positive integer having the same number of divisors as n.

Original entry on oeis.org

1, 2, 2, 4, 2, 6, 2, 6, 4, 6, 2, 12, 2, 6, 6, 16, 2, 12, 2, 12, 6, 6, 2, 24, 4, 6, 6, 12, 2, 24, 2, 12, 6, 6, 6, 36, 2, 6, 6, 24, 2, 24, 2, 12, 12, 6, 2, 48, 4, 12, 6, 12, 2, 24, 6, 24, 6, 6, 2, 60, 2, 6, 12, 64, 6, 24, 2, 12, 6, 24, 2, 60, 2, 6, 12, 12, 6, 24, 2, 48, 16, 6, 2, 60, 6, 6, 6, 24, 2
Offset: 1

Views

Author

Max Alekseyev, May 19 2008

Keywords

Comments

a(n) <= n for all n. Moreover, a(n) = n if and only if n belongs to A005179 or A007416.

Links

Crossrefs

Cf. A000005, A005179, A007416, A139770.
Cf. A019505, A138113, A061300 (sequences that can be defined in terms of this sequence).

Programs

  • Mathematica
    a140635[n_] := NestWhile[#+1&, 1, DivisorSigma[0, n]!=DivisorSigma[0, #]&]
a140635[{m_, n_}] := Map[a140635, Range[m, n]]
a140635[{1, 89}] (* Hartmut F. W. Hoft, Jun 13 2023 *)
  • PARI
    A140635(n) = { my(nd = numdiv(n)); for (i=1, n, if (numdiv(i) == nd, return (i))); }; \\ After A139770, Antti Karttunen, May 27 2017
  • Python
    from sympy import divisor_count as d
def a(n):
    x=d(n)
    m=1
    while True:
        if d(m)==x: return m
        else: m+=1 # Indranil Ghosh, May 27 2017

Formula

a(n) = A005179(A000005(n)).

A350049 a(1) = 1; for n > 1, a(n) is the smallest number with at least as many divisors as 2*a(n-1).

Original entry on oeis.org

1, 2, 4, 6, 12, 24, 48, 60, 120, 240, 360, 720, 1260, 2520, 5040, 10080, 20160, 27720, 55440, 110880, 221760, 332640, 665280, 1081080, 2162160, 4324320, 8648640, 17297280, 21621600, 43243200, 73513440, 147026880, 294053760, 367567200, 735134400, 1396755360, 2793510720
Offset: 1

Views

Author

J. Lowell, Dec 11 2021

Keywords

Comments

Identical to A019505 for 63 terms. A019505(64) = 97039187544499200 (the smallest number with exactly 63360 divisors), but a(64) = 74801040398884800 (the smallest number with at least 63360 divisors; its actual number of divisors is 64512).
Subsequence of A002182.

Links

  • Michael De Vlieger, Concordance of a(n) and A002182, n = 1..10000, terms compactified via A067255 for log_10(a(n)) > 33, giving indices in A002182 and number of divisors of first 1000 terms.

Crossrefs

Cf. A019505, A002182, A139770.

A365264 a(n) is the smallest positive integer k whose number of divisors is larger than that of n.

Original entry on oeis.org

2, 4, 4, 6, 4, 12, 4, 12, 6, 12, 4, 24, 4, 12, 12, 12, 4, 24, 4, 24, 12, 12, 4, 36, 6, 12, 12, 24, 4, 36, 4, 24, 12, 12, 12, 48, 4, 12, 12, 36, 4, 36, 4, 24, 24, 12, 4, 60, 6, 24, 12, 24, 4, 36, 12, 36, 12, 12, 4, 120, 4, 12, 24, 24, 12, 36, 4, 24, 12, 36, 4, 120, 4, 12, 24, 24, 12, 36, 4, 60
Offset: 1

Views

Author

Hartmut F. W. Hoft, Aug 29 2023

Keywords

Comments

The distinct values in this sequence together with 1 form A002182.

Links

Crossrefs

Cf. A002182, A139770, A140635.

Programs

  • Mathematica
    a365264[n_] := NestWhile[#+1&, 1, DivisorSigma[0, n]>=DivisorSigma[0, #]&]
a365264[{m_, n_}] := Map[a365264, Range[m, n]]
a365264[{1, 80}]
  • PARI
    a(n) = my(k=1, nd=numdiv(n)); while(numdiv(k) <= nd, k++); k; \\ Michel Marcus, Aug 29 2023

Formula

a(n) = Min_{ k >= 1, sigma_0(k) > sigma_0(n) }, n>=1.
A002182(n+1) = a(a(...a(1))...) with n >= 0 iterations.
Showing 1-4 of 4 results.

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

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