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Composite numbers whose prime factors all have the same digital root.
1

%I #9 Aug 31 2021 20:02:40

%S 4,8,9,16,22,25,27,32,44,49,58,64,81,88,94,115,116,121,125,128,166,

%T 169,176,188,202,205,232,242,243,256,274,289,295,301,319,332,343,346,

%U 352,361,376,382,403,404,427,454,464,484,512,517,526,529,548,553,562,565

%N Composite numbers whose prime factors all have the same digital root.

%H Harvey P. Dale, <a href="/A100657/b100657.txt">Table of n, a(n) for n = 1..1000</a>

%e 2005 = 5*401. 5 and 401 have the same digital root 5.

%e 2038 = 2*1019. 2 and 1019 have the same digital root 2.

%t sdrQ[n_]:=CompositeQ[n]&&Length[Union[1+Mod[#-1,9]&/@FactorInteger[n][[All,1]]]]==1; Select[Range[600],sdrQ] (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, Jan 11 2019 *)

%o (PARI) samedr(n) = { local(j); for(j=1,n, if(issamedr(j),print1(j",")) ) } issamedr(n) = \Test if all factors of n have the same digital root. { local(f,a,ln,x); f=0; a=ifactor(n); ln=length(a); for(x=1,ln-1, if(droot(a[x])<>droot(a[x+1]), f=1;break)); if(f==0&ln>1,return(1),return(0)) } droot(n) = \The digital root of a number. { local(x); x= n%9; if(x>0,return(x),return(9)) }

%Y Cf. A002808, A010888.

%K base,easy,nonn

%O 1,1

%A _Cino Hilliard_, Jan 02 2005