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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.
8
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
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
KEYWORD
nonn
EXTENSIONS
Offset corrected by Reinhard Zumkeller, Jun 18 2009
Name edited by Michel Marcus, Nov 12 2023
STATUS
approved