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A333221 Irregular triangle read by rows where row n lists the set of STC-numbers of permutations of the prime indices of n. 24
0, 1, 2, 3, 4, 5, 6, 8, 7, 10, 9, 12, 16, 11, 13, 14, 32, 17, 24, 18, 20, 15, 64, 21, 22, 26, 128, 19, 25, 28, 34, 40, 33, 48, 256, 23, 27, 29, 30, 36, 65, 96, 42, 35, 49, 56, 512, 37, 38, 41, 44, 50, 52, 1024, 31, 66, 80, 129, 192, 68, 72, 43, 45, 46, 53, 54, 58 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

This is a permutation of the nonnegative integers.

The k-th composition in standard order (row k of A066099) is obtained by taking the set of positions of 1's in the reversed binary expansion of k, prepending 0, taking first differences, and reversing again. We define the composition with STC-number k to be the k-th composition in standard order.

A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798.

LINKS

Table of n, a(n) for n=1..67.

EXAMPLE

Reading by columns gives:

  0  1  2  3  4  5  8  7  10  9   16  11  32  17  18  15  64  21  128  19

                 6            12      13      24  20          22       25

                                      14                      26       28

  34  33  256  23  36  65  42  35  512  37  1024  31  66  129  68  43

  40  48       27      96      49       38            80  192  72  45

               29              56       41                         46

               30                       44                         53

                                        50                         54

                                        52                         58

The sequence of terms together with the corresponding compositions begins:

     0: ()           24: (1,4)          27: (1,2,1,1)

     1: (1)          18: (3,2)          29: (1,1,2,1)

     2: (2)          20: (2,3)          30: (1,1,1,2)

     3: (1,1)        15: (1,1,1,1)      36: (3,3)

     4: (3)          64: (7)            65: (6,1)

     5: (2,1)        21: (2,2,1)        96: (1,6)

     6: (1,2)        22: (2,1,2)        42: (2,2,2)

     8: (4)          26: (1,2,2)        35: (4,1,1)

     7: (1,1,1)     128: (8)            49: (1,4,1)

    10: (2,2)        19: (3,1,1)        56: (1,1,4)

     9: (3,1)        25: (1,3,1)       512: (10)

    12: (1,3)        28: (1,1,3)        37: (3,2,1)

    16: (5)          34: (4,2)          38: (3,1,2)

    11: (2,1,1)      40: (2,4)          41: (2,3,1)

    13: (1,2,1)      33: (5,1)          44: (2,1,3)

    14: (1,1,2)      48: (1,5)          50: (1,3,2)

    32: (6)         256: (9)            52: (1,2,3)

    17: (4,1)        23: (2,1,1,1)    1024: (11)

MATHEMATICA

primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];

fbi[q_]:=If[q=={}, 0, Total[2^q]/2];

Table[Sort[fbi/@Accumulate/@Permutations[primeMS[n]]], {n, 30}]

CROSSREFS

Row lengths are A008480.

Column k = 1 is A233249.

Column k = -1 is A333220.

A related triangle for partitions is A215366.

Cf. A000120, A029931, A048793, A056239, A066099, A070939, A112798, A114994, A225620, A228351, A333218, A333219.

Sequence in context: A078840 A333658 A337598 * A334438 A185974 A129129

Adjacent sequences:  A333218 A333219 A333220 * A333222 A333223 A333224

KEYWORD

nonn,tabf

AUTHOR

Gus Wiseman, Mar 17 2020

STATUS

approved

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Last modified September 24 11:46 EDT 2021. Contains 347642 sequences. (Running on oeis4.)