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.

A358076 Numbers that share at least 1 (decimal) digit with their largest proper divisor.

Original entry on oeis.org

11, 13, 15, 17, 19, 20, 24, 25, 31, 39, 40, 41, 42, 45, 48, 50, 51, 52, 60, 61, 71, 74, 75, 80, 84, 91, 93, 94, 95, 98, 100, 101, 102, 103, 105, 107, 109, 113, 119, 120, 121, 122, 123, 124, 125, 126, 127, 131, 133, 135, 136, 137, 139, 140, 141, 142, 143, 147, 148, 149, 150
Offset: 1

Views

Author

Wesley Ivan Hurt, Oct 29 2022

Keywords

Examples

			52 is in the sequence since it shares at least one digit with 26, its largest proper divisor. Both numbers share the digit 2.

Links

Crossrefs

Cf. A032742, A357929.

Programs

  • Mathematica
    Select[Range[2, 150], Length[Intersection[IntegerDigits[#], IntegerDigits[#/FactorInteger[ #][[1, 1]]]]] > 0 &] (* Amiram Eldar, Oct 30 2022 *)
  • PARI
    isok(m) = (m>1) && #setintersect(Set(digits(m)), Set(digits(m/factor(m)[1, 1]))); \\ Michel Marcus, Oct 30 2022

A358068 Numbers that share a (decimal) digit with the sum of their proper divisors.

Original entry on oeis.org

6, 11, 12, 13, 14, 16, 17, 18, 19, 20, 21, 26, 28, 31, 32, 35, 40, 41, 42, 44, 46, 51, 56, 60, 61, 64, 68, 70, 71, 72, 74, 76, 80, 84, 86, 91, 93, 95, 96, 100, 101, 102, 103, 104, 106, 107, 108, 109, 110, 111, 112, 113, 114, 120, 121, 124, 125, 126, 127, 128, 130, 131, 132, 135, 136
Offset: 1

Views

Author

Wesley Ivan Hurt, Oct 29 2022

Keywords

Examples

			72 is in the sequence since 72 shares a digit with the sum of its proper divisors 123. Both numbers share the digit "2".

Links

Crossrefs

Cf. A001065, A357929.

Programs

  • PARI
    isok(n) = #setintersect(Set(digits(sigma(n)-n)), Set(digits(n))); \\ Michel Marcus, Oct 30 2022
  • Python
    from itertools import count, islice
from sympy import divisor_sigma
def A358068_gen(startvalue=2): # generator of terms >= startvalue
    for n in count(max(startvalue,2)):
        s = set(str(divisor_sigma(n)-n))
        if any(d in s for d in set(str(n))):
            yield n
A358068_list = list(islice(A358068_gen(),30)) # Chai Wah Wu, Oct 29 2022

A362675 Smallest number sharing n distinct (decimal) digits with its largest proper divisor.

Original entry on oeis.org

11, 125, 1025, 3105, 37125, 251748, 2051748, 20491578, 204713568, 2046913578
Offset: 1

Views

Author

Wesley Ivan Hurt, Apr 29 2023

Keywords

Examples

			------------------------------------------------
  n   a(n)    Largest proper divisor of a(n)
------------------------------------------------
  1   11                 1
  2   125                25
  3   1025               205
  4   3105               1035
  5   37125              12375
  6   251748             125874
  7   2051748            1025874
  8   20491578           10245789
  9   204713568          102356784
 10   2046913578         1023456789

Crossrefs

Cf. A032742, A358076, A357929.

Programs

  • PARI
    f(n) = n/factor(n)[1, 1]; \\ A032742
a(n) = my(k=2); while (#setintersect(Set(digits(k)), Set(digits(f(k)))) != n, k++); k; \\ Michel Marcus, Apr 29 2023
  • Python
    from sympy import factorint
from itertools import count
def a(n):
    lb = 2*int("1023456789"[:n])
    return next(k for k in count(lb) if len(set(str(k)) & set(str(k//min(factorint(k))))) == n)
print([a(n) for n in range(1, 11)]) # Michael S. Branicky, Apr 29 2023

Extensions

a(9) from Michel Marcus, Apr 29 2023
a(10) from Michael S. Branicky, Apr 29 2023
Showing 1-3 of 3 results.

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

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