A238746 Number of distinct prime signatures that occur among the divisors of the n-th prime signature number (A025487(n)).

1, 2, 3, 3, 4, 5, 5, 7, 4, 6, 6, 9, 7, 7, 9, 11, 10, 8, 12, 9, 13, 5, 10, 13, 9, 15, 14, 15, 9, 14, 16, 10, 18, 19, 17, 13, 18, 10, 19, 11, 16, 21, 12, 15, 24, 19, 17, 22, 16, 22, 12, 23, 24, 6, 19, 20, 29, 21, 21, 26, 22, 25, 13, 30, 27, 11, 26, 25, 19, 34

Offset

1,2

Comments

Also the number of members of A025487 that divide A025487(n).

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Formula

a(n) = A085082(A025487(n)) = A085082(A181822(n)).

a(n) = A322584(A025487(n)). - Amiram Eldar, Jan 21 2024

Example

5 members of A025487 divide A025487(6) = 12 (namely, 1, 2, 4, 6 and 12); therefore, a(6) = 5.

Mathematica

lpsQ[n_] := n == 1 || (Max@ Differences[(f = FactorInteger[n])[[;; , 2]]] < 1 && f[[-1, 1]] == Prime[Length[f]]); lps = Select[Range[6000], lpsQ]; c[n_] := Count[Divisors[n], _?(MemberQ[lps, #] &)]; c /@ lps  (* Amiram Eldar, Jan 21 2024 *)

Crossrefs

Cf. A085082, A025487, A181822, A322584.

Rearrangement of A115728, A115729 and A238690.

A116473(n) is the number of times n appears in the sequence.

Sequence in context: A143091 A114539 A337600 * A272611 A156562 A290736

Adjacent sequences: A238743 A238744 A238745 * A238747 A238748 A238749

Keyword

nonn

Author

Matthew Vandermast, Apr 28 2014

Status

approved