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A249809
Irregular table read by rows: T(n, k) is the number of times prime p_k has occurred as the smallest prime factor of numbers 1 .. n. (T(1,1) = 0, and for each n > 1, k = 1 .. A000720(n)).
6
0, 1, 1, 1, 2, 1, 2, 1, 1, 3, 1, 1, 3, 1, 1, 1, 4, 1, 1, 1, 4, 2, 1, 1, 5, 2, 1, 1, 5, 2, 1, 1, 1, 6, 2, 1, 1, 1, 6, 2, 1, 1, 1, 1, 7, 2, 1, 1, 1, 1, 7, 3, 1, 1, 1, 1, 8, 3, 1, 1, 1, 1, 8, 3, 1, 1, 1, 1, 1, 9, 3, 1, 1, 1, 1, 1, 9, 3, 1, 1, 1, 1, 1, 1, 10, 3, 1, 1, 1, 1, 1, 1, 10, 4, 1, 1, 1, 1, 1, 1, 11, 4, 1, 1, 1, 1, 1, 1, 11, 4, 1, 1, 1, 1, 1, 1, 1
OFFSET
1,5
COMMENTS
After the first row {0}, consists of rows of triangular table A249808 with trailing zeros removed.
FORMULA
a(n) = A249808(A249728(n), A249727(n)).
For n > 1, A078898(n) = T(n, A055396(n)).
EXAMPLE
Table begins:
k=1 2 3 4 5 6 7
n=1: 0;
n=2: 1;
n=3: 1, 1;
n=4: 2, 1;
n=5: 2, 1, 1;
n=6: 3, 1, 1;
n=7: 3, 1, 1, 1;
n=8: 4, 1, 1, 1;
n=9: 4, 2, 1, 1;
n=10: 5, 2, 1, 1;
n=11: 5, 2, 1, 1, 1;
n=12: 6, 2, 1, 1, 1;
n=13: 6, 2, 1, 1, 1, 1;
n=14: 7, 2, 1, 1, 1, 1;
n=15: 7, 3, 1, 1, 1, 1;
n=16: 8, 3, 1, 1, 1, 1;
n=17: 8, 3, 1, 1, 1, 1, 1;
...
PROG
(Scheme) (define (A249809 n) (A249808bi (A249728 n) (A249727 n))) ;; Code for A249808bi given in A249808.
CROSSREFS
A004526 gives the left edge, A001477 the row sums.
Sequence in context: A361462 A129479 A261095 * A075104 A253667 A360189
KEYWORD
nonn,tabf
AUTHOR
Antti Karttunen, Nov 06 2014
STATUS
approved