A263094 - OEIS

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).

%I #12 Oct 24 2015 12:31:37

%S 0,1,4,9,16,81,121,144,169,225,289,361,441,529,576,625,841,900,961,

%T 1024,1089,1296,1444,1521,1600,1681,1764,1849,1936,2025,2304,2401,

%U 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

%N 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).

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

%H Antti Karttunen, <a href="/A263094/b263094.txt">Table of n, a(n) for n = 0..20763</a>

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

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

%o (PARI) \\ See code in A263092.

%o (Scheme) (define (A263094 n) (A000290 (A263092 n)))

%Y Cf. A000005, A049820, A060990.

%Y Intersection of A000290 and A236562.

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

%Y Cf. A263095 (complement among squares).

%Y Cf. A262514 (a subsequence).

%Y Cf. also A263090, A263098.

%K nonn

%O 0,3

%A _Antti Karttunen_, Oct 11 2015