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 A023883 Nonprimes whose average of divisors is an integer. 7
 1, 6, 14, 15, 20, 21, 22, 27, 30, 33, 35, 38, 39, 42, 44, 45, 46, 49, 51, 54, 55, 56, 57, 60, 62, 65, 66, 68, 69, 70, 77, 78, 85, 86, 87, 91, 92, 93, 94, 95, 96, 99, 102, 105, 110, 111, 114, 115, 116, 118, 119, 123, 125, 126, 129, 132, 133, 134, 135, 138 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Nonprime numbers k such that sigma(k) == 0 (mod tau(k)). - Paolo P. Lava, Jun 11 2013 From Bernard Schott, Mar 27 2021: (Start) Some subsequences of these nonprimes arithmetic numbers. - Squares of primes of the form 6k+1 (A002476). - Cubes of odd primes (A030078 \ {8}). - Semiprimes 2*p where prime p is of the form 4k+3 (A002145). - Semiprimes 3*p where p prime <> 3 (A001748 \ {9}). - Integers 4*p where prime p is of the form 6k-1 (A007528). (End) LINKS Amiram Eldar, Table of n, a(n) for n = 1..10000 (term 1..1000 from Paolo P. Lava) EXAMPLE Sigma(22) = 36, tau(22) = 4, sigma(22)/tau(2) = 9, 22 is not prime, hence 22 belongs to this sequence. MAPLE with(numtheory); ListA023883:=proc(q) local n; for n from 1 to q do if not isprime(n) then if sigma(n) mod tau(n)=0 then print(n); fi; fi; od; end: ListA023883(10^6); # Paolo P. Lava, Jun 11 2013 MATHEMATICA Select[{Mean[Divisors[#]], #}& /@ Select[Range[140], !PrimeQ[#]&], IntegerQ[#[[1]]]&][[All, 2]] (* Jean-François Alcover, Oct 31 2017 *) CROSSREFS Intersection of A003601 and A018252. Equals A003601 \ A000040. Cf. A000005 (tau), A000203 (sigma). Cf. A001748, A002145, A002476, A007528, A030078. Sequence in context: A079010 A324814 A015822 * A230873 A192321 A190272 Adjacent sequences: A023880 A023881 A023882 * A023884 A023885 A023886 KEYWORD nonn AUTHOR Olivier Gérard STATUS approved

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Last modified November 30 03:37 EST 2023. Contains 367452 sequences. (Running on oeis4.)