cp's OEIS Frontend

A185077 Numbers such that the largest prime factor equals the sum of the squares of the other prime factors.

%I A185077 #34 Jul 28 2024 11:39:35
%S A185077 78,156,234,290,312,468,580,624,702,742,936,1014,1160,1248,1404,1450,
%T A185077 1484,1872,2028,2106,2320,2496,2808,2900,2968,3042,3744,4056,4212,
%U A185077 4498,4640,4992,5194,5616,5800,5936,6084,6318,7250,7488,8112,8410,8424,8715,8996,9126,9280,9962
%N A185077 Numbers such that the largest prime factor equals the sum of the squares of the other prime factors.
%C A185077 Observation : it seems that the prime divisors of a majority of numbers n are of the form {2, p, q} with q = 2^2 + p^2, but there exists more rarely numbers with more prime divisors (examples : 8715 = 3*5*7*83; 153230 = 2*5*7*11*199).
%C A185077 Terms which are odd: 8715, 26145, 41349, 43575, 61005, 61971, 78435, ..., . - _Robert G. Wilson v_, Jul 02 2014
%H A185077 Amiram Eldar, <a href="/A185077/b185077.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..725 from Robert Israel)
%e A185077 8996 is in the sequence because the prime divisors are {2, 13, 173} and 173 = 13^2 + 2^2.
%p A185077 filter:= proc(n)
%p A185077 local F,f,x;
%p A185077 F:= numtheory:-factorset(n);
%p A185077 f:= max(F);
%p A185077 evalb(f = add(x^2,x=F minus {f}));
%p A185077 end proc:
%p A185077 select(filter, [$1..10000]); # _Robert Israel_, Jul 02 2014
%t A185077 Reap[Do[p = First /@ FactorInteger[n]; If[p[[-1]] == Plus@@(Most[p]^2), Sow[n]], {n, 9962}]][[2, 1]]
%t A185077 lpfQ[n_]:=With[{f=FactorInteger[n][[;;,1]]},Total[Most[f]^2]==Last[f]]; Select[Range[10000],lpfQ] (* _Harvey P. Dale_, Jul 28 2024 *)
%o A185077 (PARI) isok(n) = {my(f = factor(n)); f[#f~, 1] == sum(i=1, #f~ - 1, f[i, 1]^2);} \\ _Michel Marcus_, Jul 02 2014
%Y A185077 Cf. A071140.
%Y A185077 See also the related sequences A048261, A121518.
%K A185077 nonn
%O A185077 1,1
%A A185077 _Michel Lagneau_, Feb 18 2011
%E A185077 Corrected by _T. D. Noe_, Feb 18 2011