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 1-5 of 5 results.

A194357 Triangle of divisors of 6^n, each number occurring once.

Original entry on oeis.org

1, 2, 3, 6, 4, 9, 12, 18, 36, 8, 24, 27, 54, 72, 108, 216, 16, 48, 81, 144, 162, 324, 432, 648, 1296, 32, 96, 243, 288, 486, 864, 972, 1944, 2592, 3888, 7776, 64, 192, 576, 729, 1458, 1728, 2916, 5184, 5832, 11664, 15552, 23328, 46656, 128, 384, 1152, 2187
Offset: 0

Views

Author

T. D. Noe, Aug 25 2011

Keywords

Examples

			The triangle has rows beginning with 2^k and ending with 6^k:
  1
  2,  3,  6
  4,  9,  12, 18,  36
  8,  24, 27, 54,  72,  108, 216
  16, 48, 81, 144, 162, 324, 432, 648, 1296

Links

Crossrefs

Cf. A194356 (divisors of 10^n), A194358 (divisors of 30^n).
Cf. A003586 (3-smooth numbers).

Programs

  • Mathematica
    Join[{{1}}, Table[Complement[Divisors[6^n], Divisors[6^(n-1)]], {n, 9}]]
DeleteDuplicates[Flatten[Divisors[6^Range[0,10]]]] (* Harvey P. Dale, Sep 12 2024 *)

A194358 Triangle of divisors of 30^n, each number occurring once.

Original entry on oeis.org

1, 2, 3, 5, 6, 10, 15, 30, 4, 9, 12, 18, 20, 25, 36, 45, 50, 60, 75, 90, 100, 150, 180, 225, 300, 450, 900, 8, 24, 27, 40, 54, 72, 108, 120, 125, 135, 200, 216, 250, 270, 360, 375, 500, 540, 600, 675, 750, 1000, 1080, 1125, 1350, 1500, 1800, 2250, 2700, 3000
Offset: 0

Views

Author

T. D. Noe, Aug 26 2011

Keywords

Comments

The length of row k is A003215(k), the centered hexagonal numbers, 3k^2 + 3k + 1.

Examples

			The triangle has rows beginning with 2^k and ending with 30^k:
1
2, 3, 5, 6, 10, 15, 30
4, 9, 12, 18, 20, 25, 36, 45, 50, 60, 75, 90, 100, 150, 180, 225, 300, 450, 900

Links

Crossrefs

Cf. A194356, A194357.
Cf. A051037 (5-smooth numbers).

Programs

  • Mathematica
    Join[{{1}}, Table[Complement[Divisors[30^n], Divisors[30^(n-1)]], {n, 9}]]

A194359 Triangle of divisors of 210^n, each number occurring once.

Original entry on oeis.org

1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 105, 210, 4, 9, 12, 18, 20, 25, 28, 36, 45, 49, 50, 60, 63, 75, 84, 90, 98, 100, 126, 140, 147, 150, 175, 180, 196, 225, 245, 252, 294, 300, 315, 350, 420, 441, 450, 490, 525, 588, 630, 700, 735, 882, 900
Offset: 0

Views

Author

T. D. Noe, Aug 26 2011

Keywords

Comments

The length of row k is A005917, the rhombic dodecahedral numbers, (k+1)^4 - k^4. The triangle has rows beginning with 2^k and ending with 210^k.

Links

Crossrefs

Cf. A018336, A194356, A194357, A194358.

Programs

  • Mathematica
    Join[{{1}}, Table[Complement[Divisors[210^n], Divisors[210^(n-1)]], {n, 9}]]
Take[DeleteDuplicates[Flatten[Divisors/@(210^Range[5])]],100] (* Harvey P. Dale, Sep 03 2020 *)

A167620 Numbers that are multiples of their digital product, where this digital product also appears as their least significant digits.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 15, 111, 112, 115, 315, 612, 1111, 1112, 1113, 1115, 1116, 11111, 11112, 11115, 12312, 13212, 21312, 23112, 31212, 32112, 111111, 111112, 111115, 111315, 111612, 113115, 116112, 131115, 161112, 311115, 511175
Offset: 1

Views

Author

Claudio Meller, Nov 07 2009

Keywords

Comments

Subsequence of A007602. - R. J. Mathar, Nov 12 2009
The digital products of the terms are a subsequence of A238985. - Karl-Heinz Hofmann, Feb 16 2024

Examples

			612 is in the list because 6*1*2=12, 612 is a multiple of 12, and 12 is the final two digits of 612.

Links

Crossrefs

Cf. A007602, A238985, A194356.

Programs

  • PARI
    is(n) = { my(vp = vecprod(digits(n))); vp != 0 && n %vp == 0 && n % 10^(#digits(vp)) == vp } \\ David A. Corneth, Mar 30 2021
  • Python
    A167620 = []
for k in range(1,511176):
    dprod, k_str = 1, str(k)
    for d in range(0,len(k_str)): dprod *= int(k_str[d])
    if dprod != 0 and k % dprod == 0 and str(dprod) == k_str[-(len(str(dprod))):]:
        A167620.append(k)
print(A167620) # Karl-Heinz Hofmann, Jan 26 2024

A194360 Triangle of divisors of 105^n, each number occurring once.

Original entry on oeis.org

1, 3, 5, 7, 15, 21, 35, 105, 9, 25, 45, 49, 63, 75, 147, 175, 225, 245, 315, 441, 525, 735, 1225, 1575, 2205, 3675, 11025, 27, 125, 135, 189, 343, 375, 675, 875, 945, 1029, 1125, 1323, 1715, 2625, 3087, 3375, 4725, 5145, 6125, 6615, 7875, 8575, 9261, 15435
Offset: 0

Views

Author

T. D. Noe, Sep 08 2011

Keywords

Comments

The length of row k is A003215(k), the centered hexagonal numbers, 3k^2 + 3k + 1.

Examples

			The triangle has rows beginning with 3^k and ending with 105^k:
1
3, 5, 7, 15, 21, 35, 105
9, 25, 45, 49, 63, 75, 147, 175, 225, 245, 315, 441, 525, 735, 1225, 1575, 2205, 3675, 11025

Links

Crossrefs

Cf. A194356, A194357, A194358, A194359.
Cf. A108347 (numbers of the form (3^i)*(5^j)*(7^k))

Programs

  • Mathematica
    Join[{{1}}, Table[Complement[Divisors[105^n], Divisors[105^(n-1)]], {n, 9}]]
Showing 1-5 of 5 results.

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