A063770 Numbers k such that Sum_{j=1..k} sigma(j) divides Product_{j=1..k} phi(j).
1, 28, 52, 53, 55, 63, 76, 159, 166, 176, 219, 230, 289, 302, 303, 318, 321, 327, 348, 360, 364, 365, 381, 383, 402, 417, 430, 434, 438, 444, 451, 452, 454, 465, 469, 478, 504, 512, 522, 530, 531, 557, 559, 570, 572, 584, 595, 613, 629, 631, 641, 645, 684
Offset: 1
Keywords
Links
- Harry J. Smith, Table of n, a(n) for n = 1..1000
Programs
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Mathematica
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 *) -
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
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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