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A322609 Numbers k such that s(k) = 2k, where s(k) is the sum of divisors of k that have a square factor (A162296). 1
24, 54, 112, 150, 294, 726, 1014, 1734, 1984, 2166, 3174, 5046, 5766, 8214, 10086, 11094, 13254, 16854, 19900, 20886, 22326, 26934, 30246, 31974, 32512, 37446, 41334, 47526, 56454, 61206, 63654, 68694, 71286, 76614, 96774, 102966, 112614, 115926, 133206 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

This sequence is infinite since 6*p^2 is included for all primes p. Terms that are not of the form 6*p^2: 112, 1984, 19900, 32512, 134201344, ...

Includes 4*k if k is an even perfect number: see A000396. - Robert Israel, Jan 06 2019

LINKS

Robert Israel, Table of n, a(n) for n = 1..300

MAPLE

filter:= proc(n) convert(remove(numtheory:-issqrfree, numtheory:-divisors(n)), `+`)=2*n end proc:

select(filter, [$1..200000]); # Robert Israel, Jan 06 2019

MATHEMATICA

s[1]=0; s[n_] := DivisorSigma[1, n] - Times@@(1+FactorInteger[n][[;; , 1]]); Select[Range[10000], s[#] == 2# &]

PROG

(PARI) s(n) = sumdiv(n, d, d*(1-moebius(d)^2)); \\ A162296

isok(n) = s(n) == 2*n; \\ Michel Marcus, Dec 20 2018

CROSSREFS

Cf. A000396, A013929, A162296.

Sequence in context: A294156 A108215 A038635 * A234238 A228876 A005782

Adjacent sequences:  A322606 A322607 A322608 * A322610 A322611 A322612

KEYWORD

nonn

AUTHOR

Amiram Eldar, Dec 20 2018

STATUS

approved

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Last modified November 21 06:00 EST 2019. Contains 329350 sequences. (Running on oeis4.)