A270422 Numbers n such that n = a*b and 2*n + 1 = c*d such that a + b = c + d.

7, 24, 32, 87, 104, 175, 184, 287, 335, 399, 552, 560, 759, 840, 847, 1000, 1232, 1287, 1455, 1504, 1719, 1824, 2015, 2232, 2320, 2464, 2992, 3047, 3080, 3160, 3552, 3912, 3952, 4199, 4927, 4959, 5512, 5575, 5719, 5887, 6104, 6600, 7175, 7279, 7455, 8207, 8399, 8624, 8855, 8992, 9424, 9775, 9799, 10000

Offset

1,1

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Example

n = 7 = 1*7 and 2*n + 1 = 15 = 3*5 such that 1 + 7 = 3 + 5.
n = 24 = 2*12 and 2*n + 1 = 49 = 7*7 such that 2 + 12 = 7 + 7.
n = 32 = 2*16 and 2*n + 1 = 65 = 5*13 such that 2 + 16 = 5 + 13.
n = 87 = 3*29 and 2*n + 1 = 175 = 7*25 such that 3 + 29 = 7 + 25.

Mathematica

sd[n_] := Plus @@@ ({#, n/#} & /@ Select[ Divisors@ n, #^2 <= n &]); Select[Range@ 10000, {} != Intersection[ sd[#], sd[2*# + 1]] &] (* Giovanni Resta, Jul 12 2016 *)

Prog

(PARI) is(n)=my(m=2*n+1, d=divisors(n), e=divisors(m)); for(i=1, #d, for(j=1, #e, if(d[i] + n/d[i] == e[j] + m/e[j], return(1)))); 0 \\ Charles R Greathouse IV, Jul 21 2016
(PARI) is(n)=my(m=2*n+1, d=divisors(m), t, s); for(i=1, #d, t=d[i]+m/d[i]; if(issquare(t^2 - 4*n, &s) && (t+s)*(t-s)==4*n && (t+s)%2==0, return(1))); 0 \\ Charles R Greathouse IV, Jul 21 2016

Crossrefs

Sequence in context: A287132 A287193 A076673 * A063165 A154612 A031084

Adjacent sequences: A270419 A270420 A270421 * A270423 A270424 A270425

Keyword

nonn

Author

Debapriyay Mukhopadhyay, Jul 12 2016

Extensions

Missing term 8992 from Giovanni Resta, Jul 12 2016

Status

approved