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.

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A249917 Square array read by antidiagonals where the n-th row lists the integers x such that gcd(x, sigma(x)) = n.

Original entry on oeis.org

1, 2, 10, 3, 14, 15, 4, 20, 18, 12, 5, 22, 33, 44, 95, 7, 26, 45, 48, 145, 6, 8, 34, 51, 76, 200, 30, 91, 9, 38, 69, 88, 295, 42, 196, 56, 11, 46, 72, 92, 395, 54, 273, 112, 153, 13, 52, 87, 108, 445, 66, 287, 184, 288, 40, 16, 58, 99, 124, 475, 78, 455, 248, 459, 190, 473
Offset: 1

Views

Author

Michel Marcus, Jan 14 2015

Keywords

Comments

First line is A014567 and first column is A074391.
This is a permutation of the positive integers.

Examples

			Array begins:
   1,   2,  3,    4,   5,   7,   8, ...
  10,  14,  20,  22,  26,  34,  38, ...
  15,  18,  33,  45,  51,  69,  72, ...
  12,  44,  48,  76,  88,  92, 108, ...
  95, 145, 200, 295, 395, 445, 475, ...
   6,  30,  42,  54,  66,  78, 102, ...
  91, 196, 273, 287, 455, 581, 637, ...
  56, 112, 184, 248, 368, 376, 432, ...
  ...
		

Crossrefs

Cf. A009194 (gcd(n, sigma(n))), A014567 (gcd(n, sigma(n))=1), A074391 (smallest x such that gcd(x, sigma(x)) is n),

Programs

  • PARI
    triangle(nn) = {v = vector(nn); for (n=1, nn, for (k=1, n, if (! v[k], x = 1, x = v[k] + 1); while (gcd(sigma(x), x) != k, x++); print1(x, ", "); v[k] = x;); print(););}

A324527 a(n) = the smallest number m such that gcd(sigma(m), pod(m)) = n where sigma(k) = the sum of the divisors of k (A000203) and pod(k) = the product of the divisors of k (A007955).

Original entry on oeis.org

1, 10, 15, 12, 95, 180, 91, 56, 51, 40, 473, 6, 117, 980, 135, 70, 1139, 90, 703, 290, 861, 26378, 3151, 54, 745, 468, 255, 2156, 5017, 26100, 775, 124, 1419, 2176, 4865, 96, 2701, 26714, 585, 190, 6683, 65268, 11051, 5632, 435, 144946, 13207, 42, 679, 5800
Offset: 1

Views

Author

Jaroslav Krizek, Mar 05 2019

Keywords

Comments

a(n) = the smallest number m such that A306682(m) = n.

Examples

			For n=2; a(2) = 10 because gcd(sigma(10), pod(10)) = gcd (18, 100) = 2 and 10 is the smallest.
		

Crossrefs

Programs

  • Magma
    [Min([n: n in[1..10^5] | GCD(SumOfDivisors(n), &*[d: d in Divisors(n)]) eq k]): k in [1..45]]
    
  • PARI
    f(n) = my(d=divisors(n)); gcd(vecsum(d), vecprod(d)); \\ A306682
    a(n) = {my(k=1); while (f(k) != n, k++); k;} \\ Michel Marcus, Mar 05 2019
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