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

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

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

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