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 1-7 of 7 results.

A350372 Numbers with exactly 5 semiprime divisors.

Original entry on oeis.org

180, 252, 300, 360, 396, 450, 468, 504, 540, 588, 600, 612, 684, 700, 720, 756, 792, 828, 882, 936, 980, 1008, 1044, 1080, 1100, 1116, 1176, 1188, 1200, 1224, 1300, 1332, 1350, 1368, 1400, 1404, 1440, 1452, 1476, 1500, 1512, 1548, 1575, 1584, 1620, 1656, 1692, 1700
Offset: 1

Views

Author

Wesley Ivan Hurt, Dec 27 2021

Keywords

Crossrefs

Numbers with exactly k semiprime divisors: A346041 (k=1), A345381 (k=2), A345382 (k=3), A350371 (k=4), this sequence (k=5), A350373 (k=6), A350374 (k=7), A350375 (k=8).

Programs

  • Mathematica
    q[n_] := DivisorSum[n, 1 &, PrimeOmega[#] == 2 &] == 5; Select[Range[1700], q] (* Amiram Eldar, Dec 28 2021 *)
  • PARI
    isok(k) = sumdiv(k, d, bigomega(d)==2) == 5; \\ Michel Marcus, Dec 28 2021

A350371 Numbers with exactly 4 semiprime divisors.

Original entry on oeis.org

60, 84, 90, 120, 126, 132, 140, 150, 156, 168, 198, 204, 220, 228, 234, 240, 260, 264, 270, 276, 280, 294, 306, 308, 312, 315, 336, 340, 342, 348, 350, 364, 372, 378, 380, 408, 414, 440, 444, 456, 460, 476, 480, 490, 492, 495, 516, 520, 522, 525, 528, 532, 550, 552, 558
Offset: 1

Views

Author

Wesley Ivan Hurt, Dec 27 2021

Keywords

Crossrefs

Numbers with exactly k semiprime divisors: A346041 (k=1), A345381 (k=2), A345382 (k=3), this sequence (k=4), A350372 (k=5), A350373 (k=6), A350374 (k=7), A350375 (k=8).

Programs

A350373 Numbers with exactly 6 semiprime divisors.

Original entry on oeis.org

210, 330, 390, 462, 510, 546, 570, 690, 714, 770, 798, 858, 870, 900, 910, 930, 966, 1110, 1122, 1155, 1190, 1218, 1230, 1254, 1290, 1302, 1326, 1330, 1365, 1410, 1430, 1482, 1518, 1554, 1590, 1610, 1722, 1764, 1770, 1785, 1794, 1800, 1806, 1830, 1870, 1914, 1938, 1974, 1995
Offset: 1

Views

Author

Wesley Ivan Hurt, Dec 27 2021

Keywords

Crossrefs

Numbers with exactly k semiprime divisors: A346041 (k=1), A345381 (k=2), A345382 (k=3), A350371 (k=4), A350372 (k=5), this sequence (k=6), A350374 (k=7), A350375 (k=8).

Programs

  • Mathematica
    q[n_] := DivisorSum[n, 1 &, PrimeOmega[#] == 2 &] == 6; Select[Range[2000], q] (* Amiram Eldar, Dec 28 2021 *)
  • PARI
    isok(k) = sumdiv(k, d, bigomega(d)==2) == 6; \\ Michel Marcus, Dec 28 2021

A350374 Numbers with exactly 7 semiprime divisors.

Original entry on oeis.org

420, 630, 660, 780, 840, 924, 990, 1020, 1050, 1092, 1140, 1170, 1320, 1380, 1386, 1428, 1470, 1530, 1540, 1560, 1596, 1638, 1650, 1680, 1710, 1716, 1740, 1820, 1848, 1860, 1890, 1932, 1950, 2040, 2070, 2142, 2184, 2220, 2244, 2280, 2380, 2394, 2436, 2460, 2508, 2550
Offset: 1

Views

Author

Wesley Ivan Hurt, Dec 27 2021

Keywords

Crossrefs

Numbers with exactly k semiprime divisors: A346041 (k=1), A345381 (k=2), A345382 (k=3), A350371 (k=4), A350372 (k=5), A350373 (k=6), this sequence (k=7), A350375 (k=8).

Programs

  • Mathematica
    q[n_] := DivisorSum[n, 1 &, PrimeOmega[#] == 2 &] == 7; Select[Range[2500], q] (* Amiram Eldar, Dec 28 2021 *)
  • PARI
    isok(k) = sumdiv(k, d, bigomega(d)==2) == 7; \\ Michel Marcus, Dec 28 2021

A350375 Numbers with exactly 8 semiprime divisors.

Original entry on oeis.org

1260, 1980, 2100, 2340, 2520, 2772, 2940, 3060, 3150, 3276, 3300, 3420, 3780, 3900, 3960, 4140, 4200, 4284, 4410, 4680, 4788, 4950, 5040, 5100, 5148, 5220, 5544, 5580, 5700, 5796, 5850, 5880, 5940, 6120, 6468, 6552, 6600, 6660, 6732, 6840, 6900, 7020, 7260, 7308
Offset: 1

Views

Author

Wesley Ivan Hurt, Dec 27 2021

Keywords

Crossrefs

Numbers with exactly k semiprime divisors: A346041 (k=1), A345381 (k=2), A345382 (k=3), A350371 (k=4), A350372 (k=5), A350373 (k=6), A350374 (k=7), this sequence (k=8).

Programs

  • Mathematica
    q[n_] := DivisorSum[n, 1 &, PrimeOmega[#] == 2 &] == 8; Select[Range[7500], q] (* Amiram Eldar, Dec 28 2021 *)
  • PARI
    isok(k) = sumdiv(k, d, bigomega(d)==2) == 8; \\ Michel Marcus, Dec 28 2021

A373482 Numbers k for which A003415(k) is a multiple of A001414(k), where A003415 is the arithmetic derivative, and A001414 is the sum of prime factors with multiplicity.

Original entry on oeis.org

1, 4, 6, 8, 9, 10, 14, 15, 16, 21, 22, 25, 26, 27, 32, 33, 34, 35, 36, 38, 39, 46, 49, 51, 55, 57, 58, 62, 64, 65, 69, 72, 74, 77, 81, 82, 85, 86, 87, 91, 93, 94, 95, 100, 106, 111, 112, 115, 118, 119, 121, 122, 123, 125, 126, 128, 129, 133, 134, 141, 142, 143, 145, 146, 155, 156, 158, 159, 161, 166, 169, 177, 178
Offset: 1

Views

Author

Antti Karttunen, Jun 08 2024

Keywords

Links

Crossrefs

Cf. A001414, A003415, A373481 (characteristic function).
After the initial 1, positions of 0's in A373480.
Subsequences: A176540 (k such that A003415(k) = A001414(k)), A346041.

Programs

  • Mathematica
    Select[Range[180],
  Divisible[If[#1 < 2, 0, #1  Total[#2/#1 & @@@ #2]],
    Total[Times @@@ #2]] & @@
  {#, FactorInteger[#]} &] (* Michael De Vlieger, Jun 08 2024 *)
  • PARI
    isA373482 = A373481;

A350416 Numbers with exactly 9 semiprime divisors.

Original entry on oeis.org

6300, 8820, 9900, 11700, 12600, 14700, 15300, 17100, 17640, 18900, 19404, 19800, 20700, 21780, 22050, 22932, 23400, 25200, 26100, 26460, 27900, 29400, 29700, 29988, 30420, 30492, 30600, 31500, 33300, 33516, 34200, 35100, 35280, 36300, 36900, 37800, 38700, 38808
Offset: 1

Views

Author

Wesley Ivan Hurt, Dec 29 2021

Keywords

Comments

Numbers with exactly four distinct prime divisors (cf. A033993), one of which has multiplicity 1 and the others at least 2. - David A. Corneth, Jun 10 2022

Examples

			6300 is in the sequence as 4, 6, 9, 10, 14, 15, 21, 25, 35 are the exactly 9 of its semiprime divisors. - _David A. Corneth_, Jun 10 2022

Links

Crossrefs

Numbers with exactly k semiprime divisors: A346041 (k=1), A345381 (k=2), A345382 (k=3), A350371 (k=4), A350372 (k=5), A350373 (k=6), A350374 (k=7), A350375 (k=8), this sequence (k=9).
Cf. A033993, A220264.

Programs

Showing 1-7 of 7 results.

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