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Revisions by Ilya Gutkovskiy (See also Ilya Gutkovskiy's wiki page)

(Bold, blue-underlined text is an addition; faded, red-underlined text is a deletion.)

Showing entries 1-10 | older changes
allocated for Ilya Gutkovskiy
(history; published version)
#3 by Ilya Gutkovskiy at Mon Dec 09 06:30:46 EST 2024
STATUS

editing

proposed

allocated for Ilya Gutkovskiy
(history; published version)
#3 by Ilya Gutkovskiy at Mon Dec 09 06:30:43 EST 2024
STATUS

editing

proposed

allocated for Ilya Gutkovskiy
(history; published version)
#3 by Ilya Gutkovskiy at Mon Dec 09 06:30:40 EST 2024
STATUS

editing

proposed

#2 by Ilya Gutkovskiy at Mon Dec 09 06:24:30 EST 2024
NAME

allocated for Ilya Gutkovskiy

Number of subsets of {1..n} whose arithmetic and harmonic means are both integers.

DATA

1, 2, 3, 4, 5, 8, 9, 10, 11, 13, 14, 18, 19, 21, 27, 28, 29, 48, 49, 71, 75, 78, 79, 103

OFFSET

1,2

EXAMPLE

a(6) = 8 subsets: {1}, {2}, {3}, {4}, {5}, {6}, {2, 6} and {1, 2, 3, 6}.

CROSSREFS
KEYWORD

allocated

nonn,more

AUTHOR

Ilya Gutkovskiy, Dec 09 2024

STATUS

approved

editing

#1 by Ilya Gutkovskiy at Mon Dec 09 06:24:30 EST 2024
NAME

allocated for Ilya Gutkovskiy

KEYWORD

allocated

STATUS

approved

allocated for Ilya Gutkovskiy
(history; published version)
#2 by Ilya Gutkovskiy at Mon Dec 09 06:20:52 EST 2024
NAME

allocated for Ilya Gutkovskiy

Number of compositions (ordered partitions) of n into distinct squarefree divisors of n.

DATA

1, 1, 1, 1, 0, 1, 7, 1, 0, 0, 1, 1, 24, 1, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 151, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 31, 1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 1, 1, 864, 1, 1, 0, 0, 1, 127, 1, 0, 1, 1, 1, 0, 1, 1, 0, 0, 1, 7, 1, 0

OFFSET

0,7

EXAMPLE

a(6) = 7 because we have [6], [3, 2, 1], [3, 1, 2], [2, 3, 1], [2, 1, 3], [1, 3, 2] and [1, 2, 3].

a(12) = 24 because we have [6, 3, 2, 1] and 4! = 24 permutations.

KEYWORD

allocated

nonn

AUTHOR

Ilya Gutkovskiy, Dec 09 2024

STATUS

approved

editing

#1 by Ilya Gutkovskiy at Mon Dec 09 06:20:52 EST 2024
NAME

allocated for Ilya Gutkovskiy

KEYWORD

allocated

STATUS

approved

allocated for Ilya Gutkovskiy
(history; published version)
#2 by Ilya Gutkovskiy at Mon Dec 09 06:16:29 EST 2024
NAME

allocated for Ilya Gutkovskiy

Number of compositions (ordered partitions) of n into reciprocals of positive integers <= n.

DATA

1, 5, 154, 127459

OFFSET

1,2

EXAMPLE

a(2) = 5 because we have [1/2, 1/2, 1/2, 1/2], [1/2, 1/2, 1], [1/2, 1, 1/2], [1, 1/2, 1/2] and [1, 1].

CROSSREFS
KEYWORD

allocated

nonn,more

AUTHOR

Ilya Gutkovskiy, Dec 09 2024

STATUS

approved

editing

#1 by Ilya Gutkovskiy at Mon Dec 09 06:16:29 EST 2024
NAME

allocated for Ilya Gutkovskiy

KEYWORD

allocated

STATUS

approved

Number of partitions of 1 into {1/1^2, 1/2^2, 1/3^2, ..., 1/n^2}.
(history; published version)
#13 by Ilya Gutkovskiy at Fri Nov 22 10:24:41 EST 2024
STATUS

editing

proposed