A075493 Numbers k such that (sum of digits of k) > (number of divisors of k).

3, 4, 5, 6, 7, 8, 9, 13, 14, 15, 16, 17, 18, 19, 23, 25, 26, 27, 28, 29, 31, 33, 34, 35, 37, 38, 39, 41, 43, 44, 45, 46, 47, 48, 49, 51, 52, 53, 54, 55, 56, 57, 58, 59, 61, 62, 63, 64, 65, 66, 67, 68, 69, 71, 73, 74, 75, 76, 77, 78, 79, 81, 82, 83, 85, 86, 87, 88, 89, 91, 92

Offset: 1

Author

Labos Elemer, Sep 26 2002

Keywords

• base
• easy
• nonn

Examples

			Sequence includes all primes with sum of digits > 2, i.e., all primes not of the form 10^d + 1 for nonnegative integers d (the only known primes of this form are 2, 11, and 101; see A185121).
Sequence also includes all squared primes with sum of digits > 3.
		

Crossrefs

Cf. A007953, A000005, A057531, A075492, A075491, A185121.

Programs

Mathematica

sud[x_] := Apply[Plus, IntegerDigits[x]] Do[s=sud[n]-DivisorSigma[0, n]; If[s>0, Print[n]], {n, 1, 256}]
Select[Range[100],Total[IntegerDigits[#]]>DivisorSigma[0,#]&] (* Harvey P. Dale, Mar 07 2020 *)

Formula

Solutions to A007953(k) > A000005(k).

Extensions

Edited by Jon E. Schoenfield, Sep 23 2018