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A075494
Squares whose sum of digits exceeds the number of divisors.
0
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
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
KEYWORD
base,nonn
AUTHOR
Labos Elemer, Sep 26 2002
EXTENSIONS
Edited by Jon E. Schoenfield, Sep 23 2018
STATUS
approved