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

1,1

Links

Table of n, a(n) for n=1..71.

Formula

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

Example

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.

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 *)

Crossrefs

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

Sequence in context: A096829 A265126 A039120 * A096828 A097389 A051415

Adjacent sequences: A075490 A075491 A075492 * A075494 A075495 A075496

Keyword

base,easy,nonn

Author

Labos Elemer, Sep 26 2002

Extensions

Edited by Jon E. Schoenfield, Sep 23 2018

Status

approved