A353544 -id:A353544 - cp's OEIS frontend

A353543 Primitive terms of A353537.

4, 6, 10, 14, 45, 63, 75, 105, 165, 195, 231, 242, 255, 285, 286, 345, 374, 418, 435, 442, 465, 494, 506, 598, 638, 646, 682, 754, 782, 806, 814, 874, 902, 946, 962, 1034, 1066, 1118, 1166, 1222, 1287, 1298, 1342, 1378, 1474, 1562, 1606, 1683, 1738, 1826, 1881

Offset: 1

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Amiram Eldar, Apr 25 2022

nonn

If a number is in A353537 then all its multiples are in it. Therefore, the terms of A353537 whose proper divisors are not in A353537 are the primitive terms.

			4 is a term since sigma(4)/4 = 7/4 = 1.75 > Pi^2/6 = 1.644..., the proper divisors of 4 are 1 and 2, sigma(1)/1 = 1 < Pi^2/6 and sigma(2)/2 = 3/2 < Pi^2/6.

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A000203, A013661, A353537.

Subsequences: A071395, A091191, A353544.

q[n_] := DivisorSigma[-1, n] > Pi^2/6 && AllTrue[Most @ Divisors[n], DivisorSigma[-1, #] < Pi^2/6 &]; Select[Range[2000], q]

cp's OEIS Frontend

A353543 Primitive terms of A353537.

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