A263095 Squares in A045765; numbers n^2 such that there is no such k for which k - d(k) = n^2, where d(k) is the number of divisors of k (A000005).

25, 36, 49, 64, 100, 196, 256, 324, 400, 484, 676, 729, 784, 1156, 1225, 1369, 2116, 2209, 2500, 2916, 3136, 3364, 3481, 3600, 3844, 4489, 5329, 6084, 6724, 7225, 7921, 8100, 8836, 9025, 9604, 10000, 10609, 10816, 11236, 12100, 12996, 13456, 13924, 14884, 15376, 15625, 15876, 16129, 16384, 16900, 18225, 19600, 19881, 20164, 21904, 22500, 24025, 24964, 25921, 26896

Offset: 1

Author

Antti Karttunen, Oct 10 2015

Keywords

• nonn

Comments

Some of the terms are shared with A262687, but none with A262514.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..12443

Crossrefs

Cf. A000005, A049820, A010052, A060990, A262514, A262687, A263098.

Cf. A263093 (gives the square roots).

Intersection of A000290 and A045765.

Cf. also A263091.

Programs

Mathematica

lim = 40000; Take[Select[Complement[Range@ lim, Sort@ DeleteDuplicates@ Table[n - DivisorSigma[0, n], {n, lim}]], IntegerQ@ Sqrt@ # &], 60] (* Michael De Vlieger, Oct 13 2015 *)

PARI

\\ See code in A263093.

Scheme

;; With Antti Karttunen's IntSeq-library.
(define A263095 (MATCHING-POS 1 1 (lambda (n) (and (= 1 (A010052 n)) (zero? (A060990 n))))))