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A037197 Number of divisors of sigma(n) = number of divisors of n. 7
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

R. 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.

MAPLE

A037197:= proc(n)

local i;

for i from 1 to n do if tau(i)=tau(sigma(i)) then print(i); fi; od; end:

A037197(1000); # Paolo P. Lava, Feb 12 2013

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

STATUS

approved

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Last modified September 20 13:45 EDT 2020. Contains 337264 sequences. (Running on oeis4.)