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A128251 n^4 - 1 divided by its largest fourth power divisor. 0
15, 5, 255, 39, 1295, 150, 4095, 410, 9999, 915, 20735, 1785, 38415, 3164, 65535, 5220, 104975, 8145, 159999, 12155, 234255, 17490, 331775, 24414, 456975, 33215, 614655, 44205, 809999, 57720, 1048575, 74120, 1336335, 93789, 1679615, 117135 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,1

COMMENTS

In other words, biquadratefree part of n^4-1, or biquadratefree kernel of n^4-1. Fourth power analog of what A128972 is to cubes and A068310 is to squares. A046100 Biquadratefree numbers. A008835 Largest 4th power dividing n.

LINKS

Table of n, a(n) for n=2..37.

Eric Weisstein's World of Mathematics, Biquadratefree.

FORMULA

a(n) = (n^4 - 1)/A008835(n^4 - 1) = (A000583(n)-1)/A008835((A000583(n)-1)).

EXAMPLE

a(3) = 5 because (3^4 - 1)/16 = 80/16 = (2^4 * 5)/(2^4) = 5.

a(5) = 39 because (5^4 - 1)/16 = 624/16 = (2^4 * 3 * 13)/(2^4) = 39.

a(7) = 150 because (7^4 - 1)/16 = 2400/16 = (2^5 * 3 * 5^2)/(2^4) = 150.

a(9) = 410 because (9^4 - 1)/16 = 6560/16 = (2^5 * 5 * 41)/(2^4) = 410.

a(63) = 61535 because (63^4 - 1)/256 = 15752960/256 = (2^8 * 5 * 31 * 397)/(2^8) = 61535.

CROSSREFS

Cf. A000188, A000583, A002350, A004709, A007948, A008835, A062378, A067872, A033314, A068310, A128972.

Sequence in context: A110791 A241361 A249996 * A292307 A064107 A116907

Adjacent sequences:  A128248 A128249 A128250 * A128252 A128253 A128254

KEYWORD

easy,nonn

AUTHOR

Jonathan Vos Post, May 03 2007

STATUS

approved

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Last modified July 18 01:14 EDT 2019. Contains 325110 sequences. (Running on oeis4.)