%I #34 Jul 28 2024 11:39:35

%S 78,156,234,290,312,468,580,624,702,742,936,1014,1160,1248,1404,1450,

%T 1484,1872,2028,2106,2320,2496,2808,2900,2968,3042,3744,4056,4212,

%U 4498,4640,4992,5194,5616,5800,5936,6084,6318,7250,7488,8112,8410,8424,8715,8996,9126,9280,9962

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

%C 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 Terms which are odd: 8715, 26145, 41349, 43575, 61005, 61971, 78435, ..., . - _Robert G. Wilson v_, Jul 02 2014

%H Amiram Eldar, <a href="/A185077/b185077.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..725 from Robert Israel)

%e 8996 is in the sequence because the prime divisors are {2, 13, 173} and 173 = 13^2 + 2^2.

%p filter:= proc(n)

%p local F,f,x;

%p F:= numtheory:-factorset(n);

%p f:= max(F);

%p evalb(f = add(x^2,x=F minus {f}));

%p end proc:

%p select(filter, [$1..10000]); # _Robert Israel_, Jul 02 2014

%t Reap[Do[p = First /@ FactorInteger[n]; If[p[[-1]] == Plus@@(Most[p]^2), Sow[n]], {n, 9962}]][[2, 1]]

%t lpfQ[n_]:=With[{f=FactorInteger[n][[;;,1]]},Total[Most[f]^2]==Last[f]]; Select[Range[10000],lpfQ] (* _Harvey P. Dale_, Jul 28 2024 *)

%o (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 Cf. A071140.

%Y See also the related sequences A048261, A121518.

%K nonn

%O 1,1

%A _Michel Lagneau_, Feb 18 2011

%E Corrected by _T. D. Noe_, Feb 18 2011