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 A357590 Triangular numbers which are products of five distinct primes (or pentaprimes). 0
 3570, 8778, 9870, 12090, 13530, 20706, 20910, 21945, 24090, 24310, 26565, 33670, 40470, 40755, 47586, 54285, 57630, 57970, 63546, 66430, 69006, 72390, 76245, 87990, 88410, 91806, 92235, 94395, 94830, 98790, 121278, 130305, 132870, 133386, 141778, 148785, 154290, 159330, 163878, 167910 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS A squarefree subsequence of triangular numbers (T(n) = n*(n+1)/2). LINKS Table of n, a(n) for n=1..40. EXAMPLE 3570 = 2*3*5*7*17 = 84*85/2. 21945 = 3*5*7*11*19 = 209*210/2. 121278 = 2*3*17*29*41 = 492*493/2. 154290 = 2*3*5*37*139 = 555*556/2. MAPLE q:= n-> map(i-> i[2], ifactors(n)[2])=[1\$5]: select(q, [seq(n*(n+1)/2, n=0..1000)])[]; # Alois P. Heinz, Oct 05 2022 MATHEMATICA Select[Accumulate @ Range[600], FactorInteger[#][[;; , 2]] == {1, 1, 1, 1, 1} &] (* Amiram Eldar, Oct 05 2022 *) CROSSREFS Intersection of A000217 and A046387. Cf. A068443, A128896, A333771. Sequence in context: A204600 A204599 A206090 * A071144 A204417 A204410 Adjacent sequences: A357587 A357588 A357589 * A357591 A357592 A357593 KEYWORD nonn AUTHOR Massimo Kofler, Oct 05 2022 STATUS approved

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Last modified August 9 22:05 EDT 2024. Contains 375044 sequences. (Running on oeis4.)