The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A336687 Numbers m such that tau(sigma(m)) and sigma(tau(m)) both divide m, where tau(m) is the number of divisors function (A000005) and sigma(m) is the sum of divisors function (A000203). 0
 1, 3, 4, 12, 64, 84, 140, 144, 162, 192, 336, 360, 420, 468, 480, 576, 600, 644, 720, 780, 1008, 1344, 1512, 1584, 1600, 1740, 1872, 2160, 2240, 2448, 2592, 2736, 2880, 2884, 3136, 3240, 3888, 4032, 4158, 4228, 4464, 4608, 4800, 5040, 5115, 5184, 5328, 5670, 6060, 6192, 6336 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Conjecture: The only m such that m = tau(sigma(m))*sigma(tau(m)) are in {1,468,3240}. Verified for m up to 1*10^9. - Ivan N. Ianakiev, Aug 06 2020 LINKS Table of n, a(n) for n=1..51. EXAMPLE For 84: tau(84) = 12 and sigma(12) = 28 with 84/28 = 3. Also, sigma(84) = 224 and tau(224) = 12 with 84/12 = 7. Hence, 84 is a term. MAPLE with(numtheory): filter:= m-> irem(m, tau(sigma(m)))=0 and irem(m, sigma(tau(m)))=0: select(filter, [\$1..7000])[]; MATHEMATICA Select[Range[6400], And @@ Divisible[#, {DivisorSigma[0, DivisorSigma[1, #]], DivisorSigma[1, DivisorSigma[0, #]]}] &] (* Amiram Eldar, Jul 31 2020 *) PROG (PARI) isok(m) = !(m % numdiv(sigma(m))) && !(m % sigma(numdiv(m))); \\ Michel Marcus, Aug 02 2020 CROSSREFS Cf. A000005, A000203, A062068, A062069. Intersection of A336612 and A336613. Sequence in context: A299809 A109771 A052626 * A298115 A122903 A059792 Adjacent sequences: A336684 A336685 A336686 * A336688 A336689 A336690 KEYWORD nonn AUTHOR Bernard Schott, Jul 31 2020 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 June 14 04:14 EDT 2024. Contains 373393 sequences. (Running on oeis4.)