A305215 a(n) is the number of numbers whose largest prime power factor equals A000961(n).

1, 1, 2, 2, 6, 12, 8, 16, 48, 96, 48, 240, 480, 960, 960, 960, 3840, 7680, 3072, 18432, 36864, 73728, 147456, 147456, 442368, 884736, 1769472, 589824, 4128768, 8257536, 16515072, 33030144, 16515072, 82575360, 165150720, 330301440, 660602880, 1321205760

Offset

1,3

Comments

The largest prime power factor of a number n is given by A034699(n).

Links

Table of n, a(n) for n=1..38.

Formula

a(n) = A000005(A051451(n) / A000961(n)).

Example

The first terms, alongside A000961(n) and the set of numbers k such that A034699(k) = A000961(n), are:
  n   a(n)  A000961(n)    S(n)
  --  ----  ----------    ----
   1     1           1    { 1 }
   2     1           2    { 2 }
   3     2           3    { 3, 6 }
   4     2           4    { 4, 12 }
   5     6           5    { 5, 10, 15, 20, 30, 60 }
   6    12           7    { 7, 14, 21, 28, 35, 42, 70, 84, 105, 140, 210, 420 }
   7     8           8    { 8, 24, 40, 56, 120, 168, 280, 840 }

Prog

(PARI) my(l=1); for (k=1, 103, if (omega(k) <= 1, l = lcm(l, k); print1 (numdiv(l/k) ", ")))

Crossrefs

Cf. A000005, A000961, A034699, A051451.

First differences of A056795.

Row lengths of A305325.

Sequence in context: A178802 A156992 A285529 * A219694 A054481 A262501

Adjacent sequences: A305212 A305213 A305214 * A305216 A305217 A305218

Keyword

nonn

Author

Rémy Sigrist, May 27 2018

Status

approved