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

1,2

Comments

Conjecture: sequence is infinite.

No more terms below 10^9. - Amiram Eldar, Dec 27 2018

Links

Table of n, a(n) for n=1..10.

Example

A109883(37)=36 & A109883(38)=16, both of which are squares, so 37 is a term.

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 *)

Prog

(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

Crossrefs

Cf. A110277.

Sequence in context: A352156 A284869 A057729 * A013628 A127007 A007837

Adjacent sequences: A110275 A110276 A110277 * A110279 A110280 A110281

Keyword

more,nonn

Author

Jason Earls, Jul 18 2005

Extensions

a(10) from Amiram Eldar, Dec 27 2018

Status

approved