A075494 Squares whose sum of digits exceeds the number of divisors.

4, 9, 16, 25, 49, 64, 81, 121, 169, 196, 256, 289, 361, 484, 529, 625, 676, 729, 784, 841, 961, 1089, 1156, 1225, 1369, 1444, 1681, 1849, 1936, 2116, 2209, 2401, 2809, 3025, 3249, 3364, 3481, 3721, 3844, 3969, 4096, 4225, 4489, 4624, 4761, 5041, 5329

Offset: 1

Author

Labos Elemer, Sep 26 2002

Keywords

• base
• nonn

Examples

			Sequence consists mainly of squares of primes and of special composites like 33, 34, 35, 38, 44, 46.
		

Crossrefs

Cf. A007953, A000005, A057531, A075491-A075493.

Programs

Mathematica

sud[x_] := Apply[Plus, IntegerDigits[x]] Do[s=sud[n]-DivisorSigma[0, n]; If[Greater[s, 0]&&IntegerQ[Sqrt[n]], Print[n]], {n, 1, 10000}]
Select[Range[80]^2,Total[IntegerDigits[#]]>DivisorSigma[0,#]&] (* Harvey P. Dale, Feb 16 2020 *)

Formula

Numbers k^2 such that A007953(k^2) > A000005(k^2).

Extensions

Edited by Jon E. Schoenfield, Sep 23 2018