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A301482 Composite numbers whose sum of aliquot parts divide the sum of the squares of their aliquot parts. 1
8, 22, 27, 32, 77, 125, 128, 243, 343, 494, 512, 611, 660, 1073, 1281, 1331, 1425, 2033, 2048, 2187, 2197, 2332, 3125, 4172, 4565, 4913, 5293, 6031, 6859, 8192, 9983, 12167, 13969, 15818, 15947, 16807, 17485, 19683, 23489, 23840, 24389, 25241, 25389, 29791, 32768 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Semiprimes in the sequence: 22, 77, 611, 1073, 2033, 5293, 6031, 9983, 13969, 15947, 23489, 25241, 40301, 49901, 50249, 51101, 56759, 65017, 71677, 85079, 97217, 98099, 99101, .... - Robert Israel, Mar 29 2018

LINKS

Amiram Eldar, Table of n, a(n) for n = 1..1009 (terms below 10^9, terms 1..100 from Paolo P. Lava)

EXAMPLE

Aliquot parts of 77 are 1, 7, 11. Then (1^2 + 7^2 + 11^2)/(1 + 7 + 11) = 171/19 = 9.

MAPLE

with(numtheory): P:=proc(n)

if not isprime(n) and frac((add(p^2, p=divisors(n))-n^2)/(sigma(n)-n))=0

then n; fi; end: seq(P(i), i=2..35*10^3);

MATHEMATICA

aQ[n_] := CompositeQ[n] && Divisible[DivisorSigma[2, n] - n^2, DivisorSigma[1, n] - n]; Select[Range[33000], aQ] (* Amiram Eldar, Aug 17 2019 *)

PROG

(PARI) isok(n) = (n!=1) && !isprime(n) && (((sigma(n, 2) - n^2) % (sigma(n) - n)) == 0); \\ Michel Marcus, Mar 23 2018

CROSSREFS

Cf. A001065, A001157, A020487, A067558.

Contains A056824.

Sequence in context: A304301 A236917 A064193 * A213017 A305515 A063301

Adjacent sequences:  A301479 A301480 A301481 * A301483 A301484 A301485

KEYWORD

nonn,easy

AUTHOR

Paolo P. Lava, Mar 22 2018

STATUS

approved

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Last modified October 18 12:18 EDT 2019. Contains 328160 sequences. (Running on oeis4.)