

A185077


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


3



78, 156, 234, 290, 312, 468, 580, 624, 702, 742, 936, 1014, 1160, 1248, 1404, 1450, 1484, 1872, 2028, 2106, 2320, 2496, 2808, 2900, 2968, 3042, 3744, 4056, 4212, 4498, 4640, 4992, 5194, 5616, 5800, 5936, 6084, 6318, 7250, 7488, 8112, 8410, 8424, 8715, 8996, 9126, 9280, 9962
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OFFSET

1,1


COMMENTS

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).
Terms which are odd: 8715, 26145, 41349, 43575, 61005, 61971, 78435, ..., .  Robert G. Wilson v, Jul 02 2014


LINKS

Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..725 from Robert Israel)


EXAMPLE

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


MAPLE

filter:= proc(n)
local F, f, x;
F:= numtheory:factorset(n);
f:= max(F);
evalb(f = add(x^2, x=F minus {f}));
end proc:
select(filter, [$1..10000]); # Robert Israel, Jul 02 2014


MATHEMATICA

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


PROG

(PARI) isok(n) = {my(f = factor(n)); f[#f~, 1] == sum(i=1, #f~  1, f[i, 1]^2); } \\ Michel Marcus, Jul 02 2014


CROSSREFS

Cf. A071140.
See also the related sequences A048261, A121518.
Sequence in context: A161596 A275218 A260364 * A042945 A044329 A044710
Adjacent sequences: A185074 A185075 A185076 * A185078 A185079 A185080


KEYWORD

nonn


AUTHOR

Michel Lagneau, Feb 18 2011


EXTENSIONS

Corrected by T. D. Noe, Feb 18 2011


STATUS

approved



