A377486 a(n) = product of {p^k : p | n, k = 1..floor(log n/log p)}, a(1) = 1.

1, 2, 3, 8, 5, 24, 7, 64, 27, 320, 11, 1728, 13, 448, 135, 1024, 17, 27648, 19, 5120, 189, 11264, 23, 27648, 125, 13312, 729, 7168, 29, 93312000, 31, 32768, 8019, 557056, 875, 23887872, 37, 622592, 9477, 4096000, 41, 167215104, 43, 360448, 91125, 753664, 47, 23887872

Offset: 1

Author

Michael De Vlieger, Oct 29 2024

Keywords

• nonn
• easy

Comments

Compare with A064446, where A064446(n) = Product_{p|n} p^floor(log n / log p).

Examples

			Let S(n) = row n of A377485 = { p^k : p | n, p^k <= n, k > 0 }.
a(4) = 8 since S(4) = {2, 4} and the product of these is 8.
a(6) = 24 since S(6) = {2, 3, 4} and the product of these is 24.
a(12) = 1728 since S(12) = {2, 3, 4, 8, 9}, etc.
		

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..10000
• Michael De Vlieger, Log log scatterplot of a(n), n = 1..2^20.

Crossrefs

Cf. A064446, A162306, A246655, A377485.

Programs

Mathematica

{1}~Join~Table[Times @@ Flatten@ Map[#^Range[Floor@ Log[#, n]] &, FactorInteger[n][[All, 1]]], {n, 2, 120}]

Formula

a(p) = p for prime p.

a(p^k) = Product_{j=1..k} p^j = p^(k*(k+1)/2) = p^A000217(k).

a(n) = Product_{p|n} p^(k*(k+1)/2), where k = floor(log n / log p).

Product of row n of A377485.