cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A275164 The 167 numbers n such that n(n+1) is 19-smooth.

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%I A275164 #12 Nov 14 2016 05:22:19
%S A275164 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,24,25,26,27,32,
%T A275164 33,34,35,38,39,44,48,49,50,51,54,55,56,63,64,65,75,76,77,80,84,90,95,
%U A275164 98,99,104,119,120,125,132,135,143,152,153,168,169,170,175,189,195,208,209,220,224,242,255,272,285,288,323,324,342,350,351,360,363,374,384,399,440
%N A275164 The 167 numbers n such that n(n+1) is 19-smooth.
%C A275164 See A002071.
%C A275164 The full list of 167 terms is given in the b-file (this is the 8th row of the table A138180).
%H A275164 Jean-François Alcover, <a href="/A275164/b275164.txt">Table of n, a(n) for n = 1..167</a>
%t A275164 pMax = 19; smoothMax = 10^15; smoothNumbers[p_?PrimeQ, max_] := Module[{a, aa, k, pp, iter}, k = PrimePi[p]; aa = Array[a, k]; pp = Prime[Range[k]]; iter = Table[{a[j], 0, PowerExpand@Log[pp[[j]], max/Times @@ (Take[pp, j - 1]^Take[aa, j - 1])]}, {j, 1, k}]; Table[Times @@ (pp^aa), Sequence @@ iter // Evaluate] // Flatten // Sort]; Select[(Sqrt[1 + 4*smoothNumbers[pMax, smoothMax]] - 1)/2, IntegerQ]
%Y A275164 Cf. A002071, A145604, A138180, A145605, A002072, A085152, A085153, A252493, A252492,A275156.
%K A275164 fini,full,nonn
%O A275164 1,2
%A A275164 _Jean-François Alcover_, Nov 14 2016