A110278 Values of n such that the perfect deficiency (A109883) of n and n+1 are both squares.
1, 4, 5, 16, 37, 256, 65536, 80656, 3459600, 166926400
Offset: 1
Examples
A109883(37)=36 & A109883(38)=16, both of which are squares, so 37 is a term.
Crossrefs
Cf. A110277.
Programs
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Mathematica
subtract = If[ #1 < #2, Throw[ #1], #1 - #2]&; f[n_] := Catch @ Fold[subtract, n, Divisors @ n]; a = False; Do[b = IntegerQ[ Sqrt[ f[ n]]]; If[{a, b} == {True, True}, Print[n - 1]]; a = b, {n, 10^7}] (* Robert G. Wilson v, Jul 21 2005 *) -
PARI
a109883(n) = {my(r = n); fordiv(n, d, if (r < d, return (r)); r -= d;); 0;} isok(n) = issquare(a109883(n)) && issquare(a109883(n+1)); \\ Michel Marcus, Dec 28 2018
Extensions
a(10) from Amiram Eldar, Dec 27 2018
Comments