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Amiram Eldar, <a href="/A212645/b212645.txt">Table of n, a(n) for n = 1..10000</a>

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0, 1, 2, 3, 4, 2, 5, 3, 6, 4, 4, 7, 5, 5, 8, 6, 6, 3, 9, 7, 6, 7, 4, 10, 8, 7, 8, 5, 11, 9, 8, 5, 9, 6, 8, 12, 10, 9, 6, 10, 7, 9, 13, 11, 10, 7, 6, 11, 8, 10, 7, 14, 12, 11, 8, 4, 10, 7, 12, 9, 11, 8, 15, 13, 12, 9, 5, 11, 8, 13, 10, 12, 9, 16, 14, 8, 13, 10, 6, 12, 9, 9, 14, 11, 13, 10

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The excess of n, or A046660(n), is a function of the second signature of n (cf. A212172). Since A181800 gives the first integer of each second signature, this sequence gives the value of A046660 for each second signature in order of its first appearance. a Each nonnegative integer n occurs A000041(n) is also times in the number of prime factors of A212638(n) when repetitions are countedsequence.

Each nonnegative integer n occurs A000041a(n) times in is also the sequencenumber of prime factors of A212638(n), counted with multiplicity.

a(n) = number of excess prime divisors of A181800(n) (n-th powerful number that is the first integer of each its prime signature).

0, 1, 2, 3, 4, 2, 5, 3, 6, 4, 4, 7, 5, 5, 8, 6, 6, 3, 9, 7, 6, 7, 4, 10, 8, 7, 8, 5, 11, 9, 8, 5, 9, 6, 8, 12, 10, 9, 6, 10, 7, 9, 13, 11, 10, 7, 6, 11, 8, 10, 7, 14, 12, 11, 8, 4, 10, 7, 12, 9, 11, 8, 15, 13, 12, 9, 5, 11, 8, 13, 10, 12, 9, 16, 14, 8, 13, 10, 6, 12, 9, 9, 14, 11, 13, 10, 17, 6, 12

36 (2^2*3^2, or 2*2*3*3) has 4 prime factors when repetitions are counted, but only 2 distinct prime factors. Therefore, its "excess " as defined in A046660 is (4-2) = 2. Since 36 = A181800(6), a(6) = 2.

A046660 indexed by second signature (cf. A212172): a(n) = number of excess prime divisors of A181800(n) (n-th powerful number that is the first integer of each prime signature).

The excess of n, or A046660(n) , is a function of the second signature of n (cf. A212172). The sequence Since A181800 gives the smallest first integer of each second signature, this sequence gives the value of A046660 for each second signature in order of its first appearance. a(n) is also the number of prime factors of A212638(n) when repetitions are counted.

Each nonnegative integer n occurs A000041(n) times in the sequence.

A rearrangement of A036042; each nonnegative integer n appears A000041(n) times in the sequence.

A rearrangement of A036042.

allocated for Matthew VandermastA046660 indexed by second signature (cf. A212172): a(n) = excess of A181800(n).

0, 1, 2, 3, 4, 2, 5, 3, 6, 4, 4, 7, 5, 5, 8, 6, 6, 3, 9, 7, 6, 7, 4, 10, 8, 7, 8, 5, 11, 9, 8, 5, 9, 6, 8, 12, 10, 9, 6, 10, 7, 9, 13, 11, 10, 7, 6, 11, 8, 10, 7, 14, 12, 11, 8, 4, 10, 7, 12, 9, 11, 8, 15, 13, 12, 9, 5, 11, 8, 13, 10, 12, 9, 16, 14, 8, 13, 10, 6, 12, 9, 9, 14, 11, 13, 10, 17, 6, 12

1,3

A046660(n) is a function of the second signature of n (cf. A212172). The sequence A181800 gives the smallest integer of each second signature.

a(n) = A046660(A181800(n)) = A212639(n)-A212179(n).

a(n) = A001222(A212638(n)).

36 (2^2*3^2, or 2*2*3*3) has 4 prime factors when repetitions are counted, but only 2 distinct prime factors. Therefore, its excess as defined in A046660 is (4-2) = 2. Since 36 = A181800(6), a(6) = 2.

Cf. A046660, A181800, A212172, A212176, A212179, A212638, A212639, A212647.

A rearrangement of A036042; each nonnegative integer n appears A000041(n) times in the sequence.

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nonn

Matthew Vandermast, Jun 09 2012

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