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

%I A095406 #8 Nov 21 2013 12:48:19
%S A095406 10,12,14,15,20,21,30,34,35,38,40,42,50,51,57,60,63,70,74,90,91,95,
%T A095406 100,102,104,105,106,110,111,112,114,115,116,118,119,120,122,123,126,
%U A095406 130,132,133,134,140,141,142,145,146,150,152,153,154,158,161,170,171,174
%N A095406 Numbers n such that Sum-of-digits-of-n < Sum-of-digits-of-all-distinct-prime-factors-of-n.
%F A095406 Solutions to A007953[x] < A095402[x].
%e A095406 n=38: digit sum=11, prime factor-digit sum=2+1+9=12>11, so 38 is here;
%e A095406 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].
%t A095406 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]]
%t A095406 Select[Range[200],Total[IntegerDigits[#]]<Total[Flatten[IntegerDigits/@ Transpose[FactorInteger[#]][[1]]]]&] (* _Harvey P. Dale_, May 06 2012 *)
%Y A095406 Cf. A007953, A051351, A095402, A095403, A095404, A095405.
%K A095406 base,nonn
%O A095406 1,1
%A A095406 _Labos Elemer_, Jun 21 2004