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.

A212861 Numbers n such that the sum of prime factors of n (counted with repetition) equals three times the largest prime divisor.

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%I A212861 #12 Jul 26 2016 18:11:04
%S A212861 8,24,27,125,150,160,180,343,490,588,700,840,896,945,1008,1134,1331,
%T A212861 2197,3388,3718,4840,4913,5445,5808,6292,6534,6859,8085,8624,9464,
%U A212861 9625,9702,10647,11550,12167,12274,12320,12675,13520,13750,13860,14784,15015,15028
%N A212861 Numbers n such that the sum of prime factors of n (counted with repetition) equals three times the largest prime divisor.
%C A212861 The numbers prime(n)^3 are in the sequence.
%H A212861 Charles R Greathouse IV, <a href="/A212861/b212861.txt">Table of n, a(n) for n = 1..10000</a>
%F A212861 sopfr(n) = 3*gpf(n), where gpf = A006530. - _Charles R Greathouse IV_, May 29 2012
%e A212861 150 is in the sequence because 150 = 2*3*5^2 => sum of prime divisors = 2+3 + 5*2 = 15 = 3*5 where 5 is the greatest prime divisor.
%p A212861 with(numtheory):A:= proc(n) local e, j; e := ifactors(n)[2]: add (e[j][1]*e[j][2], j=1..nops(e)) end: for m from 2 to 20000 do: x:=factorset(m):n1:=nops(x):if A(m)=3*x[n1] then printf(`%d, `,m):else fi:od:
%t A212861 spfQ[n_]:=Module[{f=FactorInteger[n]},Total[Flatten[Table[#[[1]], #[[2]]]&/@ f]]==3*f[[-1,1]]]; Select[Range[16000],spfQ] (* _Harvey P. Dale_, Jul 26 2016 *)
%o A212861 (PARI) is(n)=my(f=factor(n),k=#f[,1]); k && sum(i=1,k,f[i,1]*f[i,2]) == 3*f[k,1] \\ _Charles R Greathouse IV_, May 29 2012
%Y A212861 Cf. A001414, A163836.
%K A212861 nonn
%O A212861 1,1
%A A212861 _Michel Lagneau_, May 29 2012