A095406 Numbers n such that Sum-of-digits-of-n < Sum-of-digits-of-all-distinct-prime-factors-of-n.

10, 12, 14, 15, 20, 21, 30, 34, 35, 38, 40, 42, 50, 51, 57, 60, 63, 70, 74, 90, 91, 95, 100, 102, 104, 105, 106, 110, 111, 112, 114, 115, 116, 118, 119, 120, 122, 123, 126, 130, 132, 133, 134, 140, 141, 142, 145, 146, 150, 152, 153, 154, 158, 161, 170, 171, 174

Offset

1,1

Links

Table of n, a(n) for n=1..57.

Formula

Solutions to A007953[x] < A095402[x].

Example

n=38: digit sum=11, prime factor-digit sum=2+1+9=12>11, so 38 is here;
n=10^j:digit sum=1, prime factor-digit sum=2+5=7?1. so 10^j is here for all j [this implies that the sequence is infinite].

Mathematica

ffi[x_] :=Flatten[FactorInteger[x]] lf[x_] :=Length[FactorInteger[x]] ba[x_] :=Table[Part[ffi[x], 2*j-1], {j, 1, lf[x]}] sd[x_] :=Apply[Plus, IntegerDigits[x]] tdp[x_] :=Flatten[Table[IntegerDigits[Part[ba[x], j]], {j, 1, lf[x]}], 1] sdp[x_] :=Apply[Plus, tdp[x]] a=Table[sd[w], {w, 1, 256}]; b=Table[sdp[w], {w, 1, 150}]; b-a; Flatten[Position[Sign[b-a], -1]]
Select[Range[200], Total[IntegerDigits[#]]<Total[Flatten[IntegerDigits/@ Transpose[FactorInteger[#]][[1]]]]&] (* Harvey P. Dale, May 06 2012 *)

Crossrefs

Cf. A007953, A051351, A095402, A095403, A095404, A095405.

Sequence in context: A062408 A127653 A050705 * A337028 A050769 A330724

Adjacent sequences: A095403 A095404 A095405 * A095407 A095408 A095409

Keyword

base,nonn

Author

Labos Elemer, Jun 21 2004

Status

approved