A377844
Numbers that have a single odd exponent larger than 1 in their prime factorization.
Original entry on oeis.org
8, 24, 27, 32, 40, 54, 56, 72, 88, 96, 104, 108, 120, 125, 128, 135, 136, 152, 160, 168, 184, 189, 200, 224, 232, 243, 248, 250, 264, 270, 280, 288, 296, 297, 312, 328, 343, 344, 351, 352, 360, 375, 376, 378, 384, 392, 408, 416, 424, 432, 440, 456, 459, 472, 480, 486, 488, 500
Offset: 1
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q[n_] := Count[FactorInteger[n][[;; , 2]], _?(# > 1 && OddQ[#] &)] == 1; Select[Range[500], q]
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is(k) = #select(x -> x>1 && x%2, factor(k)[, 2]) == 1;
A384442
Smallest k such that A361373(k) = n.
Original entry on oeis.org
1, 2, 4, 6, 10, 12, 18, 40, 36, 30, 60, 102, 84, 132, 150, 264, 210, 540, 330, 420, 660, 630, 840, 1050, 2100, 2340, 2520, 3150, 2310, 2730, 4290, 4620, 6930, 9240, 15960, 16170, 17850, 18480, 20790, 34650, 62370, 68250, 30030, 62790, 60060, 78540, 90090, 117810
Offset: 0
Table of n, a(n) for n = 1..12, showing row a(n) of A377485.
log n/log p
n a(n) p_1 p_2 p_3 row n of A377485
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1: 2 1 {p}
2: 4 2 {p, p^2}
3: 6 2 1 {p, q, p^2}
4: 10 3 1 {p, p^2, q, p^3}
5: 12 3 2 {p, q, p^2, p^3, q^2}
6: 18 4 2 {p, q, p^2, p^3, q^2, p^4}
7: 40 5 2 {p, p^2, q, p^3, p^4, q^2, p^5}
8: 36 5 3 {p, q, p^2, p^3, q^2, p^4, q^3, p^5}
9: 30 4 3 2 {p, q, p^2, r, p^3, q^2, p^4, r^2, q^3}
10: 60 5 3 2 {p, q, p^2, r, p^3, q^2, p^4, r^2, q^3, p^5}
11: 102 6 4 1 {p, q, p^2, p^3, q^2, p^4, r, q^3, p^5, p^6, q^4}
12: 84 6 4 2 {p, q, p^2, r, p^3, q^2, p^4, q^3, p^5, r^2, p^6, q^4}
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nn = 30030; t[_] := 0; u = 1; Do[(If[t[#] == 0, t[#] = n]; If[# == u, While[t[u] != 0, u++]]) &[Total@ Map[Floor@ Log[#, n] &, FactorInteger[n][[All, 1]] ] ], {n, 2, nn}]; {1}~Join~Array[t, u - 1]
Showing 1-2 of 2 results.
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