A080371 a(n) is the smallest x such that the quotient d(x+1)/d(x) equals n, where d = A000005.

2, 1, 11, 23, 47, 59, 191, 167, 179, 239, 5119, 359, 20479, 2111, 719, 839, 983039, 1259, 786431, 3023, 2879, 15359, 62914559, 3359, 22031, 266239, 6299, 6719, 13690208255, 5039, 22548578303, 7559, 156671, 6881279, 25919, 10079, 1168231104511, 5505023, 479231, 21839

Offset: 1

Author

Labos Elemer, Feb 24 2003

Keywords

• nonn

Comments

a(37) > 10^12. - Donovan Johnson, Sep 02 2013

Conjecture: a(p) = 2^(p-1) * k - 1 for some k > 0 and prime p. - David A. Corneth, Jan 26 2021

Examples

			n = 49: a(49) = 233279 = m, d(m+1) = 98, d(m) = 2, quotient = 49.
		

Links

• David A. Corneth, Table of n, a(n) for n = 1..196
• Donovan Johnson, All 435 terms <= 10^12

Crossrefs

Cf. A000005, A080372.

Programs

Mathematica

t = Table[ 0, {50}]; Do[ s = DivisorSigma[0, n+1] / DivisorSigma[0, n]; If[ s < 51 && t[[s]] == 0, t[[s]] = n], {n, 1, 10^8}]; t

PARI

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

Formula

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

a(n) = A086551(n) - 1. - Hugo Pfoertner, Jan 26 2021

Extensions

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

a(29) and a(31) from Donovan Johnson, Dec 26 2012

More terms from David A. Corneth, Jan 27 2021