A353543 - OEIS

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

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OFFSET

1,1

COMMENTS

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.

LINKS

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

EXAMPLE

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.

MATHEMATICA

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

CROSSREFS

Cf. A000203, A013661, A353537.

Subsequences: A071395, A091191, A353544.

Sequence in context: A188592 A188586 A084372 * A140611 A333846 A076957

Adjacent sequences: A353540 A353541 A353542 * A353544 A353545 A353546

KEYWORD

nonn

AUTHOR

Amiram Eldar, Apr 25 2022

STATUS

approved