Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #5 Oct 15 2013 22:32:25
%S 1,4,6,8,9,16,18,24,25,26,27,28,32,33,36,39,44,45,46,48,49,52,54,55,
%T 56,62,64,65,66,68,69,72,75,76,77,78,80,81,82,86,87,88,92,93,96,98,99,
%U 108,117,121,124,125,128,129,135,138,143,144,147,148,155,156,159,162,164
%N Numbers n such that Sum-of-digits-of-n > Sum-of-digits-of-all-distinct-prime-factors-of-n.
%F Solutions to A007953[x]>A095402[x].
%e n=24: digit sum=6, prime factor-digit sum=2+3=5, so 24 is here;
%e n=153: digit sum=9, prime factor-digit sum=3+5+3=11>9, so 153 is here.
%t 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]]
%Y Cf. A007953, A051351, A095402, A095403, A095405, A095406.
%K nonn,base
%O 1,2
%A _Labos Elemer_, Jun 21 2004