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A330992
Least positive integer with exactly prime(n) factorizations into factors > 1, or 0 if no such integer exists.
8
4, 8, 16, 24, 60, 0, 0, 96, 0, 144, 216, 0, 0, 0, 288, 0, 0, 0, 768, 0, 0, 0, 0, 0, 864, 8192, 0, 0, 1080, 0, 0, 0, 1800, 3072, 0, 0, 0, 0, 0, 0, 0, 2304, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3456, 0, 3600, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 24576
OFFSET
1,1
LINKS
R. E. Canfield, P. Erdős and C. Pomerance, On a Problem of Oppenheim concerning "Factorisatio Numerorum", J. Number Theory 17 (1983), 1-28.
EXAMPLE
Factorizations of the initial positive terms are:
4 8 16 24 60 96
2*2 2*4 2*8 3*8 2*30 2*48
2*2*2 4*4 4*6 3*20 3*32
2*2*4 2*12 4*15 4*24
2*2*2*2 2*2*6 5*12 6*16
2*3*4 6*10 8*12
2*2*2*3 2*5*6 2*6*8
3*4*5 3*4*8
2*2*15 4*4*6
2*3*10 2*2*24
2*2*3*5 2*3*16
2*4*12
2*2*3*8
2*2*4*6
2*3*4*4
2*2*2*12
2*2*2*2*6
2*2*2*3*4
2*2*2*2*2*3
CROSSREFS
All positive terms belong to A025487 and also A033833.
Factorizations are A001055, with image A045782, with complement A330976.
Numbers whose number of partitions is prime are A046063.
Numbers whose number of strict partitions is prime are A035359.
Numbers whose number of set partitions is prime are A051130.
Numbers with a prime number of factorizations are A330991.
The least number with exactly 2^n factorizations is A330989(n).
Sequence in context: A343421 A337353 A368614 * A246067 A161226 A369566
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jan 07 2020
EXTENSIONS
More terms from Jinyuan Wang, Jul 07 2021
STATUS
approved