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A212644 If an integer's second signature (cf. A212172) is the n-th to appear among positive integers, a(n) = number of distinct second signatures represented among its divisors. 5
1, 2, 3, 4, 5, 3, 6, 5, 7, 7, 6, 8, 9, 9, 9, 11, 12, 4, 10, 13, 10, 15, 7, 11, 15, 14, 18, 10, 12, 17, 18, 9, 21, 13, 15, 13, 19, 22, 14, 24, 14, 18, 10, 12, 17, 18, 9, 21, 13, 15, 13, 19, 22, 14, 24, 16, 20, 14, 21, 26, 19, 10, 27, 19, 25, 16, 15, 23, 30, 24 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Also, number of divisors of A181800(n) that are members of A181800.

Consider a member of A181800 with second signature {S} whose divisors represent a total of k distinct second signatures and a total of (j+k) distinct prime signatures (cf. A212642).  Let m be any integer with second signature {S}.  Then A212180(m) = k and A085082(m) is congruent to j modulo k. If {S} is the second signature of A181800(n), then A085082(m) is congruent to A212643(n) modulo a(n).

LINKS

Table of n, a(n) for n=1..70.

FORMULA

a(n) = A212180(A181800(n)).

EXAMPLE

The divisors of 72 represent 5 distinct second signatures (cf. A212172), as can be seen from the exponents >=2, if any, in the canonical prime factorization of each divisor:

{ }: 1, 2 (prime), 3 (prime), 6 (2*3)

{2}: 4 (2^2), 9 (3^2), 12 (2^2*3), 18 (2*3^2)

{3}: 8 (2^3), 24 (2^3*3)

{2,2}: 36 (2^2*3^2)

{3,2}: 72 (2^3*3^2)

Since 72 = A181800(8), a(8) = 5.

CROSSREFS

Cf. A181800, A085082, A212172, A212176, A212642, A212643.

Sequence in context: A117607 A215092 A194551 * A278057 A088492 A025492

Adjacent sequences:  A212641 A212642 A212643 * A212645 A212646 A212647

KEYWORD

nonn

AUTHOR

Matthew Vandermast, Jun 07 2012

STATUS

approved

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Last modified May 25 01:28 EDT 2019. Contains 323534 sequences. (Running on oeis4.)