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Numbers k such that (sum of digits of k) > (number of divisors of k).
3

%I #12 Mar 07 2020 18:24:11

%S 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,

%T 38,39,41,43,44,45,46,47,48,49,51,52,53,54,55,56,57,58,59,61,62,63,64,

%U 65,66,67,68,69,71,73,74,75,76,77,78,79,81,82,83,85,86,87,88,89,91,92

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

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

%e 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).

%e Sequence also includes all squared primes with sum of digits > 3.

%t sud[x_] := Apply[Plus, IntegerDigits[x]] Do[s=sud[n]-DivisorSigma[0, n]; If[s>0, Print[n]], {n, 1, 256}]

%t Select[Range[100],Total[IntegerDigits[#]]>DivisorSigma[0,#]&] (* _Harvey P. Dale_, Mar 07 2020 *)

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

%K base,easy,nonn

%O 1,1

%A _Labos Elemer_, Sep 26 2002

%E Edited by _Jon E. Schoenfield_, Sep 23 2018