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A308968
Table, read by rows: row n contains the prime factors of A001008(n) (numerator of n-th harmonic number), with multiplicity.
5
1, 3, 11, 5, 5, 137, 7, 7, 3, 11, 11, 761, 7129, 11, 11, 61, 97, 863, 13, 13, 509, 29, 43, 919, 1049, 1117, 29, 41233, 17, 17, 8431, 37, 1138979, 19, 19, 39541, 37, 7440427, 5, 11167027, 18858053, 3, 23, 23, 53, 227, 761, 583859, 5, 577, 467183, 109, 312408463
OFFSET
1,2
COMMENTS
Row 1 is taken to be {1} instead of being empty, by convention.
Length, first = smallest and last = largest term of the rows are given in A308967, A308970 and A308971, respectively. See A308969 for prime divisors without repetition.
EXAMPLE
n | A001008(n) written as product of primes
-----+---------------------------------------------
1 | 1 (empty product)
2 | 3
3 | 11
4 | 5 * 5
5 | 137
6 | 7 * 7
7 | 3 * 11 * 11
8 | 761
9 | 7129
10 | 11 * 11 * 61
11 | 97 * 863
12 | 13 * 13 * 509
13 | 29 * 43 * 919
14 | 1049 * 1117
15 | 29 * 41233
16 | 17 * 17 * 8431
17 | 37 * 1138979
18 | 19 * 19 * 39541
19 | 37 * 7440427
20 | 5 * 11167027
etc.
PROG
(PARI) A308968_row(n)={if(n>1, concat(apply(f->vector(f[2], i, f[1]), Col(factor(A001008(n)))~)), [1])}
CROSSREFS
Cf. A001008, A308967 (row lengths, for n > 1).
Cf. A308969 (prime divisors without repetition), A308970 (column 1 = first / smallest term of each row), A308971 (last / greatest term in each row).
Sequence in context: A210610 A188950 A357115 * A084466 A084462 A156320
KEYWORD
nonn,tabf
AUTHOR
M. F. Hasler, Jul 03 2019
STATUS
approved