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A359445
Numbers k such that the sums (with multiplicity) of prime factors of k and k+1 are both squares.
1
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
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
Sequence in context: A132828 A296899 A257021 * A306223 A023690 A101745
KEYWORD
nonn
AUTHOR
Robert Israel, Jan 01 2023
STATUS
approved