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

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A342083 Number of chains of strictly inferior divisors from n to 1. 23
 1, 1, 1, 1, 1, 2, 1, 2, 1, 2, 1, 3, 1, 2, 2, 2, 1, 3, 1, 3, 2, 2, 1, 4, 1, 2, 2, 3, 1, 4, 1, 3, 2, 2, 2, 4, 1, 2, 2, 4, 1, 5, 1, 3, 3, 2, 1, 6, 1, 3, 2, 3, 1, 5, 2, 4, 2, 2, 1, 7, 1, 2, 3, 3, 2, 5, 1, 3, 2, 4, 1, 8, 1, 2, 3, 3, 2, 5, 1, 6, 2, 2, 1, 7, 2, 2, 2 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,6 COMMENTS We define a divisor d|n to be strictly inferior if d < n/d. Strictly inferior divisors are counted by A056924 and listed by A341674. These chains have first-quotients (in analogy with first-differences) that are term-wise > their decapitation (maximum element removed). Equivalently, x > y^2 for all adjacent x, y. For example, the divisor chain q = 60/6/2/1 has first-quotients (10,3,2), which are > (6,2,1), so q is counted under a(60). Also the number of factorizations of n where each factor is greater than the product of all previous factors. LINKS FORMULA G.f.: x + Sum_{k>=1} a(k) * x^(k*(k + 1)) / (1 - x^k). - Ilya Gutkovskiy, Nov 03 2021 EXAMPLE The a(n) chains for n = 2, 6, 12, 24, 42, 48, 60, 72:   2/1  6/1    12/1    24/1    42/1      48/1      60/1      72/1        6/2/1  12/2/1  24/2/1  42/2/1    48/2/1    60/2/1    72/2/1               12/3/1  24/3/1  42/3/1    48/3/1    60/3/1    72/3/1                       24/4/1  42/6/1    48/4/1    60/4/1    72/4/1                               42/6/2/1  48/6/1    60/5/1    72/6/1                                         48/6/2/1  60/6/1    72/8/1                                                   60/6/2/1  72/6/2/1                                                             72/8/2/1 The a(n) factorizations for n = 2, 6, 12, 24, 42, 48, 60, 72:   2  6    12   24    42     48     60      72      2*3  2*6  3*8   6*7    6*8    2*30    8*9           3*4  4*6   2*21   2*24   3*20    2*36                2*12  3*14   3*16   4*15    3*24                      2*3*7  4*12   5*12    4*18                             2*3*8  6*10    6*12                                    2*3*10  2*4*9                                            2*3*12 MATHEMATICA cen[n_]:=If[n==1, {{1}}, Prepend[#, n]&/@Join@@cen/@Select[Divisors[n], # 1 summing to n. A207375 lists central divisors. A253249 counts strict chains of divisors. A334996 counts ordered factorizations by product and length. A334997 counts chains of divisors of n by length. A342086 counts chains of divisors with strictly increasing quotients > 1. - Inferior: A033676, A066839, A072499, A161906. - Superior: A033677, A070038, A161908. - Strictly Inferior: A060775, A070039, A333806, A341674. - Strictly Superior: A048098, A064052, A140271, A238535, A341673. Cf. A000203, A001248, A002033, A006530, A018819, A020639, A045690, A337105, A342087, A342094, A342095, A342096, A342097. Sequence in context: A140774 A345345 A056924 * A316364 A318357 A323091 Adjacent sequences:  A342080 A342081 A342082 * A342084 A342085 A342086 KEYWORD nonn AUTHOR Gus Wiseman, Feb 28 2021 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 15 00:08 EDT 2022. Contains 356122 sequences. (Running on oeis4.)