A377486 - OEIS

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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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

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

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.

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).