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%I #16 Feb 28 2024 19:08:01
%S 1,28,52,53,55,63,76,159,166,176,219,230,289,302,303,318,321,327,348,
%T 360,364,365,381,383,402,417,430,434,438,444,451,452,454,465,469,478,
%U 504,512,522,530,531,557,559,570,572,584,595,613,629,631,641,645,684
%N Numbers k such that Sum_{j=1..k} sigma(j) divides Product_{j=1..k} phi(j).
%H Harry J. Smith, <a href="/A063770/b063770.txt">Table of n, a(n) for n = 1..1000</a>
%t Module[{nn=700,s,p},s=Accumulate[DivisorSigma[1,Range[nn]]];p=FoldList[ Times,EulerPhi[ Range[nn]]]; Position[ Thread[{s,p}],_?(Mod[#[[2]],#[[1]]]==0&),1,Heads->False]]//Flatten (* _Harvey P. Dale_, Feb 28 2024 *)
%o (PARI) j=[]; for(n=1,1300,a=sum(k=1,n, sigma(k)); b=prod(k=1,n,eulerphi(k)); if(Mod(b,a)==0,j=concat(j,n))); j
%o (PARI) { n=0; s=0; p=1; for (m=1, 10^9, s+=sigma(m); p*=eulerphi(m); if(p%s == 0, write("b063770.txt", n++, " ", m); if (n==1000, break)) ) } \\ _Harry J. Smith_, Aug 30 2009
%Y Cf. A001088, A024916.
%K nonn
%O 1,2
%A _Jason Earls_, Aug 15 2001