A374295 a(n) is the smallest positive integer k such that A096936(k) = n.

1, 7, 4, 91, 2401, 28, 117649, 1729, 196, 31213, 282475249, 364, 13841287201, 1529437, 9604, 53599, 33232930569601, 2548, 1628413597910449, 593047, 470596, 3672178237, 3909821048582988049, 6916, 68574961, 179936733613, 33124, 29059303, 459986536544739960976801, 124852

Offset: 1

Author

Seiichi Manyama, Jul 02 2024

Keywords

• nonn

Comments

a(n) is the smallest positive integer k such that A033716(k) = 2*n,

Examples

			   n        |        a(n)
------------+-------------------------------------
   2        |            7.
   3 = 3*1  |            4.
   4        |           91 =     7 * 13.
   5        |         2401 =     7^4.
   6 = 3*2  |           28 = 4 * 7.
   7        |       117649 =     7^6.
   8        |         1729 =     7 * 13 * 19.
   9 = 3*3  |          196 = 4 * 7^2.
  10        |        31213 =     7^4 * 13.
  11        |    282475249 =     7^10.
  12 = 3*4  |          364 = 4 * 7 * 13.
  13        |  13841287201 =     7^12.
  14        |      1529437 =     7^6 * 13.
  15 = 3*5  |         9604 = 4 * 7^4.
  16        |        53599 =     7 * 13 * 19 * 31.
  17        |                    7^16.
  18 = 3*6  |         2548 = 4 * 7^2 * 13.
  19        |                    7^18.
  20        |       593047 =     7^4 * 13 * 19.
  21 = 3*7  |       470596 = 4 * 7^6.
  22        |   3672178237 =     7^10 * 13.
  23        |                    7^22.
  24 = 3*8  |         6916 = 4 * 7 * 13 * 19.
  25        |     68574961 =     7^4 * 13^4.
  26        | 179936733613 =     7^12 * 13.
  27 = 3*9  |        33124 = 4 * 7^2 * 13^2.
  28        |     29059303 =     7^6 * 13 * 19.
  29        |                    7^28.
  30 = 3*10 |       124852 = 4 * 7^4 * 13.
		

Crossrefs

Cf. A033716, A096936, A343771.

Formula

If p is prime, a(p) = 7^(p-1).

a(n) is divisible by 7 for n > 3.