A237433 Canonical index of prime signature of n.

1, 2, 2, 3, 2, 4, 2, 5, 3, 4, 2, 6, 2, 4, 4, 8, 2, 4, 2, 6, 4, 4, 2, 9, 3, 4, 5, 6, 2, 7, 2, 13, 4, 4, 4, 10, 2, 4, 4, 9, 2, 7, 2, 6, 6, 4, 2, 14, 3, 4, 4, 6, 2, 7, 4, 9, 4, 4, 2, 11, 2, 4, 6, 20, 4, 7, 2, 6, 4, 7, 2, 15, 2, 4, 4, 6, 4, 7, 2, 14, 8, 4, 2, 11, 4, 4, 4, 9, 2, 7, 4, 6, 4, 4, 4, 21, 2, 4, 6, 10

Offset: 1

Author

Sung-Hyuk Cha, Feb 07 2014

Keywords

• nonn

Comments

Index of prime signature of n when prime signatures are listed in "canonical" order as defined in the "Canonical ordering of the partitions" link.

Note that A236515 uses a different ordering (see 2nd link).

Examples

			a(7) = a({1}) = 2, a(180) = a({2,2,1}) = 17, a(216) = a({3,3}) = 24
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a(1) = 1,
For all n in A000040, prime_signature(n) = {1}, a(n) = 2,
For all n in A001248, prime_signature(n) = {2}, a(n) = 3,
For all n in A006881, prime_signature(n) = {1,1}, a(n) = 4,
For all n in A030078, prime_signature(n) = {3}, a(n) = 5,
For all n in A054753, prime_signature(n) = {2,1}, a(n) = 6,
For all n in A007304, prime_signature(n) = {1,1,1}, a(n) = 7, etc.
		

Links

• OEIS Wiki, Canonical ordering of the partitions
• OEIS Wiki, Orderings of prime signature

Crossrefs

Cf. A236515.