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A305325 Irregular triangle read by rows T(n, k), n >= 1 and 1 <= k <= A305215(n): T(n, k) is the k-th positive number with largest prime power factor equal to A000961(n).

%I A305325 #9 Nov 23 2020 17:08:04
%S A305325 1,2,3,6,4,12,5,10,15,20,30,60,7,14,21,28,35,42,70,84,105,140,210,420,
%T A305325 8,24,40,56,120,168,280,840,9,18,36,45,63,72,90,126,180,252,315,360,
%U A305325 504,630,1260,2520,11,22,33,44,55,66,77,88,99,110,132,154,165
%N A305325 Irregular triangle read by rows T(n, k), n >= 1 and 1 <= k <= A305215(n): T(n, k) is the k-th positive number with largest prime power factor equal to A000961(n).
%C A305325 The largest prime power factor of a number n is given by A034699(n).
%C A305325 When interpreted as a flat sequence we obtain a permutation of the natural numbers.
%H A305325 Rémy Sigrist, <a href="/A305325/b305325.txt">Table of n, a(n) for n = 1..15360</a>
%H A305325 Rémy Sigrist, <a href="/A305325/a305325.gp.txt">PARI program for A305325</a>
%H A305325 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%F A305325 T(n, 1) = A000961(n).
%F A305325 T(n, A305215(n)) = A051451(n).
%e A305325 Triangle begins:
%e A305325   1: [1]
%e A305325   2: [2]
%e A305325   3: [3, 6]
%e A305325   4: [4, 12]
%e A305325   5: [5, 10, 15, 20, 30, 60]
%e A305325   6: [7, 14, 21, 28, 35, 42, 70, 84, 105, 140, 210, 420]
%e A305325   7: [8, 24, 40, 56, 120, 168, 280, 840]
%e A305325   8: [9, 18, 36, 45, 63, 72, 90, 126, 180, 252, 315, 360, 504, 630, 1260, 2520]
%o A305325 (PARI) See Links section.
%Y A305325 Cf. A000961, A034699, A051451, A305215, A336816 (inverse).
%K A305325 nonn,tabf
%O A305325 1,2
%A A305325 _Rémy Sigrist_, May 30 2018