

A240062


Square array read by antidiagonals in which T(n,k) is the nth number j with the property that the symmetric representation of sigma(j) has k parts.


17



1, 2, 3, 4, 5, 9, 6, 7, 15, 21, 8, 10, 25, 27, 63, 12, 11, 35, 33, 81, 147, 16, 13, 45, 39, 99, 171, 357, 18, 14, 49, 51, 117, 189, 399, 903, 20, 17, 50, 55, 153, 207, 441, 987, 2499, 24, 19, 70, 57, 165, 243, 483, 1029, 2709, 6069, 28, 22, 77, 65, 195, 261, 513, 1113
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OFFSET

1,2


COMMENTS

This is a permutation of the positive integers.
All odd primes are in column 2 (together with some even composite numbers) because the symmetric representation of sigma(prime(i)) is [m, m], where m = (1 + prime(i))/2, for i >= 2.
The union of all oddindexed columns gives A071562, the positive integers that have middle divisors. The union of all evenindexed columns gives A071561, the positive integers without middle divisors.  Omar E. Pol, Oct 01 2018


LINKS

Table of n, a(n) for n=1..63.
Index entries for sequences that are permutations of the natural numbers


EXAMPLE

Array begins:
1, 3, 9, 21, 63, 147, 357, 903, 2499, 6069...
2, 5, 15, 27, 81, 171, 399, 987, 2709...
4, 7, 25, 33, 99, 189, 441, 1029...
6, 10, 35, 39, 117, 207, 483...
8, 11, 45, 51, 153, 243...
12, 13, 49, 55, 165...
16, 14, 50, 57...
18, 17, 70...
20, 19...
24...


CROSSREFS

For programs see A237271 and A237593.
Row 1 is A239663.
Column 1 is A238443 = A174973.
Column 2 is A239929.
Column 3 is A279102, and column 4 is A280107.  Omar E. Pol, Dec 27 2016
For more information see A239663 and A239665.
Cf. A000203, A006254, A065091, A067742, A071561, A071562, A196020, A236104, A235791, A237048, A237270, A237271, A238443, A239660, A239929, A239931A239934, A245092, A262626, A319529, A319796, A319801, A319802.
Sequence in context: A166276 A101544 A171100 * A255129 A119586 A095904
Adjacent sequences: A240059 A240060 A240061 * A240063 A240064 A240065


KEYWORD

nonn,tabl


AUTHOR

Omar E. Pol, Apr 06 2014


EXTENSIONS

a(n) > 128 from Michel Marcus, Apr 08 2014


STATUS

approved



