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%I #9 May 10 2018 17:41:31
%S 180224,257499,579375,1075599,1990575,2353616,5598800,10320624,
%T 11560400,13975983,16951599,17213552,17651600,17672499,17784207,
%U 20626991,20660624,21041775,21912848,22252400,24533199,24953103,26161875,26604207,29232175,29253392
%N Numbers n such that n and n+1 both have 30 divisors.
%H Charles R Greathouse IV, <a href="/A274365/b274365.txt">Table of n, a(n) for n = 1..10000</a>
%t SequencePosition[Table[If[DivisorSigma[0,n]==30,1,0],{n,3*10^7}],{1,1}][[All,1]] (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, May 10 2018 *)
%o (PARI) is(n)=numdiv(n)==30 && numdiv(n+1)==30
%o (PARI) list(lim)=my(v=List(),t); forprime(p=2,sqrtnint(lim\2,14), my(p14=p^14); forprime(q=2,lim\p14, if(p==q, next); t=p14*q; if(numdiv(t+1)==30, listput(v,t)); if(numdiv(t-1)==30, listput(v,t-1)))); forprime(p=2,sqrtnint(lim\4,9), my(p9=p^9); forprime(q=2,sqrtint(lim\p9), if(p==q, next); t=p9*q^2; if(numdiv(t+1)==30, listput(v,t)); if(numdiv(t-1)==30, listput(v,t-1)))); forprime(p=2,sqrtnint(lim\16,5), my(p5=p^5); forprime(q=2,sqrtnint(lim\p5,4), if(p==q, next); t=p5*q^4; if(numdiv(t+1)==30, listput(v,t)); if(numdiv(t-1)==30, listput(v,t-1)))); forprime(p=2,sqrtnint(lim\12,4), my(p4=p^4); forprime(q=2,sqrtint(lim\p4\2), if(p==q, next); my(q2=q^2); forprime(r=2,lim\p4\q2, if(p==r || q==r, next); t=p4*q2*r; if(numdiv(t+1)==30, listput(v,t)); if(numdiv(t-1)==30, listput(v,t-1))))); Set(v)
%Y Intersection of A005237 and A137493.
%Y Cf. A000005, A274357.
%K nonn
%O 1,1
%A _Charles R Greathouse IV_, Jun 19 2016
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