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A360661
Number of factorizations of n into a prime number of factors > 1.
1
0, 0, 0, 1, 0, 1, 0, 2, 1, 1, 0, 3, 0, 1, 1, 3, 0, 3, 0, 3, 1, 1, 0, 5, 1, 1, 2, 3, 0, 4, 0, 5, 1, 1, 1, 7, 0, 1, 1, 5, 0, 4, 0, 3, 3, 1, 0, 9, 1, 3, 1, 3, 0, 5, 1, 5, 1, 1, 0, 9, 0, 1, 3, 7, 1, 4, 0, 3, 1, 4, 0, 12, 0, 1, 3, 3, 1, 4, 0, 9, 3, 1, 0, 9, 1, 1, 1, 5, 0, 9, 1, 3, 1, 1, 1, 13, 0, 3, 3, 7
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OFFSET
1,8
COMMENTS
From Bernard Schott, Mar 25 2023: (Start)
a(n) depends only on the prime signature of n.
a(n) = 0 iff n is in A008578 (1 with primes).
a(n) = 1 iff n is in A001358 (semiprimes).
a(n) = 2 iff n is in A030078 (p^3).
a(n) = 3 iff n is in A080258 (p^4 or p*q^2).
a(n) = 4 iff n is in A007304 (p*q*r). (End)
LINKS
Table of n, a(n) for n=1..100.
Sean A. Irvine, Java program (github)
Eric Weisstein's World of Mathematics, Unordered Factorization
FORMULA
From Bernard Schott, Mar 25 2023: (Start)
a(A000040(n)) = 0.
a(A001248(n)) = a(A006881(n)) = 1.
a(A030514(n)) = a(A054753(n)) = 3. (End)
EXAMPLE
a(2) = 0 since 2 = 2 is the unique factorization of 2.
a(4) = 1 since 4 = 2^2 = 2 * 2.
a(6) = 1 since 6 = 2 * 3.
a(8) = 2 since 8 = 2^3 = 2 * 4 = 2 * 2 * 2.
a(12) = 3 since 12 = 3 * 2^2 = 2 * 6 = 3 * 4 = 2 * 2 * 3.
a(16) = 3 since 16 = 2^4 = 2 * 8 = 4 * 4 = 2 * 2 * 4.
a(30) = 4 since 30 = 2 * 3 * 5 = 2 * 15 = 3 * 10 = 5 * 6.
CROSSREFS
Cf. A001055, A038499, A339890.
Cf. A001248, A001358, A006881, A007304, A008578, A030078, A030514, A054753, A080258.
Sequence in context: A337345 A294904 A055212 * A028422 A064577 A371729
Adjacent sequences: A360658 A360659 A360660 * A360662 A360663 A360664
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Feb 15 2023
STATUS
approved

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Last modified December 11 07:47 EST 2024. Contains 378604 sequences.
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