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A357606 Primitive terms of A357605: numbers in A357605 with no proper divisor in A357605. 1
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 (list; graph; refs; listen; history; text; internal format)
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
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
KEYWORD
nonn
AUTHOR
Amiram Eldar, Oct 06 2022
STATUS
approved

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Last modified April 15 05:45 EDT 2024. Contains 371667 sequences. (Running on oeis4.)