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
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, ...
...
Cf.
A009194 (gcd(n, sigma(n))),
A014567 (gcd(n, sigma(n))=1),
A074391 (smallest x such that gcd(x, sigma(x)) is n),
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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
For n=2; a(2) = 10 because gcd(sigma(10), pod(10)) = gcd (18, 100) = 2 and 10 is the smallest.
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[Min([n: n in[1..10^5] | GCD(SumOfDivisors(n), &*[d: d in Divisors(n)]) eq k]): k in [1..45]]
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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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