The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation. Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A146556 Natural growth of an aliquot sequence driven by a perfect number 2^(p-1)*((2^p) - 1). 4
 3, 5, 7, 9, 17, 19, 21, 43, 45, 111, 193, 195, 477, 927, 1777, 1779, 2973, 4963, 6397, 6399, 12961, 14983, 14985, 40191, 66993, 114063, 193233, 334959, 558273, 951999, 1586673, 3724815, 8255985, 18271887, 31279473, 66853647, 171456753, 339654927 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS This is the natural growth of an aliquot sequence that has a driver of the form 2^(p-1) * ((2^p) - 1) (Perfect Number). It will continue growing this way until it loses the driver, which can only happen when the next term and the driver are not coprimes (which hardly ever happens). The natural growth of the aliquot sequence starting with p=5 at 2^(p-1)*(2^p-1)*3 = 496*3 = 1488 has the factors 3, 5, 7, 9, 17, 19, 21, 43, 45, 111, 193, 195, 477, 927, 1777, 1779, 2973, 4963, 6397, 6399, 12961, 14983, 14985, 40191, 66993, 114063, 193233, 334959, 558273, 951999, 1586673, 3564018 and "loses the driver" at the next term because it is not a multiple of 496. I complemented the terms therefore from p=7 and initial factor 3 which does not lose the driver early. - R. J. Mathar, Jan 22 2009 LINKS Mathworld, Aliquot Sequence Stern, Aliquot Sequences from the trenches [broken link?] FORMULA a(n) = a(n-1) + 2*(sigma(a(n-1)) - a(n-1)). - Roderick MacPhee, Aug 21 2012 EXAMPLE The aliquot sequence starting at 1488 (2^4*31*3) is: 1488, 2480, 3472, 4464,8432, 9424 or: 496*3, 496*5, 496*7, 496*9, 496*17, 496*19, always keeping the 496 driver until reaching a term that is not coprime with 496. MAPLE p := 7: dr := 2^(p-1)*(2^p-1) ; f := 3 ; aliq := proc(n) option remember ; global dr, f ; local an_1 ; if n = 1 then dr*f ; else an_1 := procname(n-1) ; numtheory[sigma](an_1)-an_1 ; fi; end: A := proc(n) option remember ; global dr ; aliq(n)/dr ; end: for n from 1 to 70 do printf("%a, ", A(n)) ; od: # R. J. Mathar, Jan 22 2009 MATHEMATICA NestList[2*DivisorSigma[1, #]-#&, 3, 40] (* Harvey P. Dale, Jul 16 2013 *) PROG (PARI) A146556()=a=; until(#a==79, a=concat(a, a[#a]+2*(sigma(a[#a])-a[#a]))); a (PARI) a(n)=if(n==1, 3, 2*sigma(a(n-1))-a(n-1)) \\ R. K. Guy, Jul 16 2013 CROSSREFS Cf. A000396, A008892, A215778, A216224. Sequence in context: A240944 A117913 A064411 * A084229 A191356 A144753 Adjacent sequences:  A146553 A146554 A146555 * A146557 A146558 A146559 KEYWORD hard,nonn AUTHOR Sergio Pimentel, Oct 31 2008 EXTENSIONS More terms, as derived from p=7, driver 8128. - R. J. Mathar, Jan 22 2009 STATUS approved

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

Last modified July 2 02:03 EDT 2020. Contains 335389 sequences. (Running on oeis4.)