A063891 - OEIS

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A063891

Numbers k such that nusigma(usigma(k)) = 2k, where usigma(k) is the sum of unitary divisors of k (A034448) and nusigma(k) is the sum of non-unitary divisors of k (A048146).

1631, 2016, 8928, 11808, 36576, 45360, 1486080, 2359008, 3093552, 37748448, 101350656, 150994656, 2885670144

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OFFSET

1,1

COMMENTS

a(14) > 2*10^11. All the numbers of the form 2^5 * 3^2 * p where p>3 is a Mersenne prime (A000668) are in the sequence, so a(14) <= 618475290336. - Giovanni Resta, Apr 10 2019

LINKS

Table of n, a(n) for n=1..13.

MATHEMATICA

usigma[1] = 1; usigma[n_] := Times @@ (1 + Power @@@ FactorInteger[n]); nusigma[n_] := DivisorSigma[1, n] - usigma[n]; Select[Range[12000], nusigma[usigma[#]] == 2# &] (* Amiram Eldar, Apr 10 2019 *)

PROG

(PARI) u(n) = sumdiv(n, d, if(gcd(d, n/d)==1, d));

z(n)=sigma(n)-u(n) ;

for(n=1, 10^8, if(z(u(n))==2*n, print1(n, ", ")))

CROSSREFS

Cf. A000203, A034448, A048146, A019284, A063885.

Sequence in context: A241493 A328452 A202985 * A254849 A237923 A297659

Adjacent sequences: A063888 A063889 A063890 * A063892 A063893 A063894

KEYWORD

more,nonn

AUTHOR

Jason Earls, Aug 28 2001

EXTENSIONS

More terms from Thomas Baruchel, Oct 22 2003

a(11)-a(13) from Amiram Eldar, Apr 10 2019

STATUS

approved