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

0,3

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

Formula

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

Mathematica

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

Prog

(PARI) \\ See code in A263092.
(Scheme) (define (A263094 n) (A000290 (A263092 n)))

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.

Sequence in context: A038784 A038239 A352919 * A226354 A299921 A089149

Adjacent sequences: A263091 A263092 A263093 * A263095 A263096 A263097

Keyword

nonn

Author

Antti Karttunen, Oct 11 2015

Status

approved