The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A046985 Multiply perfect numbers whose average divisor is an integer and divides the number itself. 10
 1, 6, 672, 30240, 32760, 23569920, 45532800, 14182439040, 51001180160, 153003540480, 403031236608, 13661860101120, 154345556085770649600, 9186050031556349952000, 143573364313605309726720, 352338107624535891640320, 680489641226538823680000, 34384125938411324962897920 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Amiram Eldar, Table of n, a(n) for n = 1..321 FORMULA Let s1 = sigma(k) = A000203(k) be the sum of divisors of k and s0 = d(k) = A000005(k) be the number of divisors of k. Then, k is a term if s1/k, (k * s0)/s1, and s1/s0 are all integers. EXAMPLE k = 45532800 is a term since, s0 = 384, s1 = 182131200, and the three quotients s1/k = 182131200/45532800 = 4, (k * s0)/s1 = (45532800 * 384)/182131200 = 96, and s1/s0 = 182131200/384 = 474300 are all integers. MATHEMATICA q[n_] := Module[{d = DivisorSigma[0, n], s = DivisorSigma[1, n]}, Divisible[s, n] && Divisible[n * d, s] && Divisible[s, d]]; Select[Range[33000], q] (* Amiram Eldar, May 09 2024 *) PROG (PARI) isok(n) = s1 = sigma(n); s0 = numdiv(n); !(s1 % n) && !(s1 % s0) && !((n*s0) % s1); \\ Michel Marcus, Dec 10 2013 (PARI) is(k) = {my(f = factor(k), s = sigma(f), d = numdiv(f)); !(s % k) && !((k * d) % s) && !(s % d); } \\ Amiram Eldar, May 09 2024 CROSSREFS Intersection of A003601, A007691 and A001599. Cf. A000005, A000203, A046986, A046987. Sequence in context: A269842 A333639 A331724 * A159371 A159620 A125535 Adjacent sequences: A046982 A046983 A046984 * A046986 A046987 A046988 KEYWORD nonn AUTHOR Labos Elemer EXTENSIONS a(10)-a(15) from Donovan Johnson, Nov 30 2008 Edited and a(16)-a(18) added by Amiram Eldar, May 09 2024 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified August 4 13:32 EDT 2024. Contains 374921 sequences. (Running on oeis4.)