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
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.
Programs
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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 *)
Extensions
Edited by Jon E. Schoenfield, Sep 23 2018