A095405 - OEIS

%I #8 Sep 29 2019 14:45:02

%S 2,3,5,7,11,13,17,19,22,23,29,31,37,41,43,47,53,58,59,61,67,71,73,79,

%T 83,84,85,89,94,97,101,103,107,109,113,127,131,136,137,139,149,151,

%U 157,160,163,166,167,173,179,181,191,193,197,199,202,211,223,227,229,233,234

%N Numbers n such that Sum-of-digits-of-n = Sum-of-digits-of-all-distinct-prime-factors-of-n.

%H Harvey P. Dale, <a href="/A095405/b095405.txt">Table of n, a(n) for n = 1..1000</a>

%F Solutions to A007953[x]=A095402[x].

%e n=85: digit sum=13, prime factor-digit sum=5+1+7=13, so 85 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], 0]]

%t Select[Range[2,300],Total[Flatten[IntegerDigits/@FactorInteger[#][[All, 1]]]] == Total[IntegerDigits[#]]&] (* _Harvey P. Dale_, Sep 29 2019 *)

%Y Cf. A007953, A051351, A095402, A095403, A095404, A095406.

%K nonn,base

%O 1,1

%A _Labos Elemer_, Jun 21 2004