A357606 Primitive terms of A357605: numbers in A357605 with no proper divisor in A357605.

36, 48, 80, 120, 162, 168, 200, 224, 264, 270, 280, 300, 312, 352, 378, 392, 408, 416, 450, 456, 500, 552, 588, 594, 630, 696, 700, 702, 744, 750, 882, 888, 918, 968, 980, 984, 1026, 1032, 1050, 1088, 1100, 1128, 1216, 1232, 1242, 1272, 1300, 1372, 1416, 1452

Offset

1,1

Comments

Numbers k such that A162296(k) > 2*k but for all the aliquot divisors d of k (i.e., d | k, d < k), A162296(d) <= 2*d.

If k is a term then all the positive multiples of k are terms of A357605.

The least odd term is a(144) = 4725.

Links

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

Example

36 is a term since A162296(36) = 79 > 2*36, but for all the divisors d of 36, 1, 2, 3, 4, 6, 9, 12 and 18, A162296(d) <= 2*d. E.g., A162296(18) = 28 < 2*18.

Mathematica

q[n_] := Module[{f = FactorInteger[n], p, e}, p = f[[;; , 1]]; e = f[[;; , 2]]; Times @@ ((p^(e + 1) - 1)/(p - 1)) - Times @@ (p + 1) > 2*n]; q[1] = False; primQ[n_] := q[n] && AllTrue[Most @ Divisors[n], ! q[#] &]; Select[Range[1500], primQ]

Crossrefs

Cf. A162296.

Subsequence of A005101, A013929 and A357605.

Similar sequences: A091191, A302574.

Sequence in context: A357605 A064597 A119850 * A348274 A033701 A349869

Adjacent sequences: A357603 A357604 A357605 * A357607 A357608 A357609

Keyword

nonn

Author

Amiram Eldar, Oct 06 2022

Status

approved