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

1,1

Links

Table of n, a(n) for n=1..47.

Formula

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

Example

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

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 *)

Crossrefs

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

Sequence in context: A188061 A279456 A069560 * A063735 A056798 A036454

Adjacent sequences: A075491 A075492 A075493 * A075495 A075496 A075497

Keyword

base,nonn

Author

Labos Elemer, Sep 26 2002

Extensions

Edited by Jon E. Schoenfield, Sep 23 2018

Status

approved