A080372 a(n) is the smallest x such that the quotient d(x)/d(x+1) equals n, where d = A000005.

2, 6, 12, 30, 112, 60, 192, 210, 180, 240, 13312, 420, 12288, 2112, 1008, 1320, 2162688, 1800, 786432, 2160, 4800, 15360, 62914560, 2520, 6480, 61440, 6300, 8640, 3489660928, 12240, 3221225472, 7560, 64512, 1376256, 58320, 12600, 206158430208, 8650752, 184320, 15120

Offset: 1

Author

Labos Elemer, Feb 24 2003

Keywords

• nonn

Comments

a(41) > 10^12. - Donovan Johnson, Sep 02 2013

Examples

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

Links

• Donovan Johnson, All 433 terms <= 10^12

Crossrefs

Cf. A000005, A080371.

Programs

Mathematica

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

PARI

{a(n) = my(k=1); while(numdiv(k)!=n*numdiv(k+1), k++); k} \\ Seiichi Manyama, Jan 17 2021

Formula

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

Extensions

More terms from Robert G. Wilson v, Feb 27 2003

a(23), a(29) and a(31) from Donovan Johnson, Jun 02 2010

a(37), a(39)-a(40) from Donovan Johnson, Sep 02 2013