A200145
Primitive (squarefree) elements of A199745.
Original entry on oeis.org
2145, 2730, 4641, 4845, 5005, 5610, 7410, 8778, 9177, 11305, 11730, 13485, 13585, 17017, 20010, 20930, 21489, 21505, 23529, 26445, 29946, 31465, 31857, 32538, 33649, 34410, 35409, 35581, 36685, 38570, 38874, 41106, 42441, 43401, 45066, 46189, 46345, 47730, 49569
Offset: 1
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Filter:= proc(n) local F;
F:= ifactors(n)[2];
if max(seq(f[2],f=F)) > 1 or nops(F) < 4 then return false fi;
F:= map(t -> t[1],F);
convert(F,`+`) = 2*(max(F)+min(F));
end proc:
select(Filter,[$1..10^5]); # Robert Israel, Dec 31 2015
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Select[Range[50000],Max@@Last/@(fi=FactorInteger[#])==1&&Plus@@(pl=First/@fi)/2==pl[[1]]+pl[[-1]]&] (*Ray Chandler, Nov 14 2011*)
A199857
Numbers such that the sum of the squares of the largest and the smallest prime divisor equals the sum of the squares of the other distinct prime divisors.
Original entry on oeis.org
24871, 81719, 81809, 88711, 174097, 198679, 201761, 256151, 273581, 290191, 329681, 405449, 422807, 428281, 472549, 572663, 592999, 604279, 620977, 701561, 728119, 752191, 770431, 876641, 898909, 1011839, 1063517, 1121729, 1178879, 1218679, 1251439, 1389223
Offset: 1
24871 is in the sequence because the prime distinct divisors are {7, 11, 17, 19} and 19^2 + 7^2 = 11^2 + 17^2 = 410.
Although the early terms are all odd with four distinct prime factors, 7212590 = 2 * 5 * 7 * 11 * 17 * 19 * 29 has seven distinct prime factors, and 2^2 + 29^2 = 5^2 + 7^2 + 11^2 + 17^2 + 19^2 = 845. - _D. S. McNeil_, Nov 12 2011
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isA199857 := proc(n)
local p;
p := sort(convert((numtheory[factorset](n)), list)) ;
if nops(p) >= 3 then
return ( op(1, p)^2 + op(-1, p)^2 = add(op(i, p)^2, i=2..nops(p)-1) ) ;
else
false;
end if;
end proc:
for n from 2 to 1500000 do
if isA199857(n) then
printf("%d, ", n) ;
end if ;
end do: # program from R. J. Mathar adapted for this sequence - see A199745
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Select[Range[1400000], Plus@@((pl=First/@FactorInteger[#])^2/2) == pl[[1]]^2+pl[[-1]]^2&] (* program from Ray Chandler adapted for this sequence - see A199745 *)
A199924
Numbers k such that the sum of the largest and the smallest prime divisor of k^2 + 1 equals the sum of the other distinct prime divisors.
Original entry on oeis.org
948, 1560, 1772, 2153, 2697, 8487, 11293, 12553, 13236, 18065, 32247, 36984, 40452, 43999, 55945, 94536, 100512, 107607, 127224, 134223, 214641, 218783, 366937, 425808, 429855, 595471, 620865, 645327, 757382, 850416, 875784, 1241106, 1330849, 1363977, 1387689
Offset: 1
2697 is in the sequence because 2697^2 + 1 = 7273810 has five distinct divisors 2, 5, 41, 113, 157 and 157 + 2 = 5 + 41 + 113 = 159.
Showing 1-3 of 3 results.
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