A037197 Numbers k such that tau(sigma(k)) = tau(k) where tau(k) is the number of divisors of k and sigma(k) their sum.

1, 2, 8, 12, 32, 52, 75, 84, 90, 98, 128, 150, 156, 338, 360, 392, 525, 528, 560, 600, 722, 867, 912, 972, 1050, 1352, 1452, 1456, 1525, 1734, 1922, 2064, 2160, 2340, 2400, 2888, 2890, 3050, 3120, 3216, 3698, 3744, 3872, 4080, 4144, 4200, 4500, 4575

Offset

1,2

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..1000

Formula

Solutions to A000005(x) = A062068(x) = A000005[A000203(x)]

Conjecture: for n > 10^6, a(n) < n^2. - Benoit Cloitre, Aug 24 2002

Example

x = 75: D[75] = {1, 3, 5, 15, 25, 75}, D[sigma(75)] = D[124] = {1, 2, 4, 31, 62, 124}, both x and sigma[x] have 6 divisors, so 75 is here.

Mathematica

Do[s=DivisorSigma[0, DivisorSigma[1, n]]; s0=DivisorSigma[0, n]; If[Greater[s0, s], Print[n]], {n, 1, 1000}]

Prog

(PARI) is(n)=numdiv(sigma(n))==numdiv(n) \\ Charles R Greathouse IV, Feb 13 2013

Crossrefs

Cf. A000005, A000203, A062068, A073802-A073804.

Sequence in context: A126775 A306898 A069185 * A125712 A062290 A176961

Adjacent sequences: A037194 A037195 A037196 * A037198 A037199 A037200

Keyword

nonn

Author

Naohiro Nomoto

Extensions

Offset corrected by Reinhard Zumkeller, Jun 18 2009

Name edited by Michel Marcus, Nov 12 2023

Status

approved