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A258106 Number x such that sigma(x) = usigma(x) + (-1)sigma(x), where sigma(x) is the sum of divisors of x (A000203), usigma(x) is the sum of unitary divisors of x (A034448) and (-1)sigma(x) is defined in A049060. 2
1998, 3876, 4524, 10062, 21582, 45220, 52780, 85428, 125976, 226100, 263900, 271092, 511428, 597012, 602946, 839106, 1033974, 1130500, 1274724, 1280532, 1319500, 1435764, 1469720, 1575860, 1810926, 1895706, 2171364, 2550636, 3162740, 4083366, 4766034, 5652500 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The definition implies that the terms of the sequence could be defined as the numbers x such that (-1)sigma(x) is equal to the sum of the non-unitary divisors of x.

LINKS

Amiram Eldar, Table of n, a(n) for n = 1..1000

EXAMPLE

usigma(1998) = 3192, (-1)sigma(1998) = 1368 and 3191 + 1368 = 4560 = sigma(1998);

usigma(3876) = 7200, (-1)sigma(3876) = 2880 and 7200 + 2880 = 10080 = sigma(3876);

usigma(4524) = 8400, (-1)sigma(4524) = 3360 and 8400 + 3360 = 11760 = sigma(4524); etc.

MAPLE

with(numtheory): P:=proc(q) local a, b, c, d, i, k, n; a:=0; b:=0;

for n from 1 to q do a:=divisors(n); d:=0; for k from 1 to nops(a) do

if gcd(a[k], n/a[k])>1 then d:=d+a[k]; fi; od; a:=ifactors(n)[2]; b:=1;

for i from 1 to nops(a) do b:=b*(-1+sum(a[i][1]^j, j=1..a[i][2])); od;

if b=d then print(n); fi; od; end: P(10^9);

MATHEMATICA

aQ[n_] := Module[{f = FactorInteger[n]}, p = f[[;; , 1]]; e = f[[;; , 2]]; Times@@((p^(e+1)-1)/(p-1)) == Times@@(p^e+1) + Times@@((p^(e+1)-2*p+1)/(p-1))]; Select[Range[2, 100000], aQ] (* Amiram Eldar, Jun 25 2019 *)

CROSSREFS

Cf. A000203, A034448, A049060, A258101.

Sequence in context: A063054 A296826 A171467 * A253744 A253751 A031808

Adjacent sequences:  A258103 A258104 A258105 * A258107 A258108 A258109

KEYWORD

nonn

AUTHOR

Paolo P. Lava, May 20 2015

EXTENSIONS

More terms from Amiram Eldar, Jun 25 2019

STATUS

approved

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Last modified December 3 14:51 EST 2020. Contains 338906 sequences. (Running on oeis4.)