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

1,1

Comments

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

Links

Table of n, a(n) for n=1..40.

Donovan Johnson, All 433 terms <= 10^12

Formula

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

Example

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

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

Prog

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

Crossrefs

Cf. A000005, A080371.

Sequence in context: A022916 A073949 A367336 * A335287 A322804 A163087

Adjacent sequences: A080369 A080370 A080371 * A080373 A080374 A080375

Keyword

nonn

Author

Labos Elemer, Feb 24 2003

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

Status

approved