A359445 Numbers k such that the sums (with multiplicity) of prime factors of k and k+1 are both squares.

255, 290, 323, 578, 1484, 2219, 2418, 2491, 4370, 4706, 5243, 6075, 7139, 7930, 9378, 10082, 10554, 10603, 12716, 15872, 16739, 18146, 18938, 22424, 22842, 25227, 25283, 25959, 26910, 28364, 28448, 30255, 33669, 33698, 34316, 34317, 38895, 40179, 41261, 43343, 43999, 47384, 60400, 62695, 64970

Offset

1,1

Comments

Numbers k such that k and k+1 are both in A051448.

Numbers k such that k, k+1 and k+2 are all in A051448 include 34316, 594044, and 869123. Are there numbers k for which k, k+1, k+2 and k+3 are all in A051448?

Links

Robert Israel, Table of n, a(n) for n = 1..750

Example

a(3) = 323 is a term because 323 = 17*19 with 17+19 = 36 = 6^2 and 324 = 2^2*3^4 with 2*2 + 4*3 = 16 = 4^2.

Maple

A:= select(proc(n) local t; issqr(add(t[1]*t[2], t=ifactors(n)[2])) end proc, {$1..10^5}):
B:= A intersect map(`-`, A, 1):
sort(convert(B, list));

Mathematica

Module[{nn=65000, sq}, sq=Table[If[IntegerQ[Sqrt[Total[Times@@@FactorInteger[n]]]], 1, 0], {n, nn}]; SequencePosition[sq, {1, 1}]][[;; , 1]] (* Harvey P. Dale, Apr 12 2024 *)

Crossrefs

Cf. A001414, A051448.

Sequence in context: A132828 A296899 A257021 * A306223 A023690 A101745

Adjacent sequences: A359442 A359443 A359444 * A359446 A359447 A359448

Keyword

nonn

Author

Robert Israel, Jan 01 2023

Status

approved