A263094 Squares in A236562; numbers n^2 such that there is at least one such k for which k - d(k) = n^2, where d(k) is the number of divisors of k (A000005).

0, 1, 4, 9, 16, 81, 121, 144, 169, 225, 289, 361, 441, 529, 576, 625, 841, 900, 961, 1024, 1089, 1296, 1444, 1521, 1600, 1681, 1764, 1849, 1936, 2025, 2304, 2401, 2601, 2704, 2809, 3025, 3249, 3721, 3969, 4096, 4225, 4356, 4624, 4761, 4900, 5041, 5184, 5476, 5625, 5776, 5929, 6241, 6400, 6561, 6889, 7056, 7396, 7569, 7744, 8281, 8464, 8649, 9216, 9409, 9801, 10201, 10404, 11025

Offset: 0

Author

Antti Karttunen, Oct 11 2015

Keywords

• nonn

Comments

Starting offset is zero, because a(0)=0 is a special case in this sequence.

Links

• Antti Karttunen, Table of n, a(n) for n = 0..20763

Crossrefs

Cf. A000005, A049820, A060990.

Intersection of A000290 and A236562.

Cf. A263092 (gives the square roots of these terms).

Cf. A263095 (complement among squares).

Cf. A262514 (a subsequence).

Cf. also A263090, A263098.

Programs

Mathematica

Take[Select[Sort@ DeleteDuplicates@ Table[n - DivisorSigma[0, n], {n, 20000}], IntegerQ@ Sqrt@ # &], 68] (* Michael De Vlieger, Oct 13 2015 *)

PARI

\\ See code in A263092.

Scheme

(define (A263094 n) (A000290 (A263092 n)))

Formula

a(n) = A000290(A263092(n)).