A080372 - OEIS

%I #17 Jan 17 2021 11:08:36

%S 2,6,12,30,112,60,192,210,180,240,13312,420,12288,2112,1008,1320,

%T 2162688,1800,786432,2160,4800,15360,62914560,2520,6480,61440,6300,

%U 8640,3489660928,12240,3221225472,7560,64512,1376256,58320,12600,206158430208,8650752,184320,15120

%N a(n) is the smallest x such that the quotient d(x)/d(x+1) equals n, where d = A000005.

%C a(41) > 10^12. - _Donovan Johnson_, Sep 02 2013

%H Donovan Johnson, <a href="/A080372/a080372.txt">All 433 terms <= 10^12</a>

%F a(n)=Min{x : d[x]/d[x+1]=n}

%e n = 17: a(17) = 2162688 = m, d(m) = 68, d(m+1) = 4, quotient = 17.

%t t = Table[ 0, {50}]; Do[ s = DivisorSigma[0, n] / DivisorSigma[0, n+1]; If[ s < 51 && t[[s]] == 0, t[[s]] = n], {n, 1, 45000000}]; t

%o (PARI) {a(n) = my(k=1); while(numdiv(k)!=n*numdiv(k+1), k++); k} \\ _Seiichi Manyama_, Jan 17 2021

%Y Cf. A000005, A080371.

%K nonn

%O 1,1

%A _Labos Elemer_, Feb 24 2003

%E More terms from _Robert G. Wilson v_, Feb 27 2003

%E a(23), a(29) and a(31) from _Donovan Johnson_, Jun 02 2010

%E a(37), a(39)-a(40) from _Donovan Johnson_, Sep 02 2013