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

Author

Rémy Sigrist, May 27 2018

Keywords

• nonn

Comments

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

Examples

			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 }
		

Crossrefs

Cf. A000005, A000961, A034699, A051451.

First differences of A056795.

Row lengths of A305325.

Programs

PARI

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

Formula

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