A090881 - OEIS

A090881

Suppose n=(p1^e1)(p2^e2)... where p1,p2,... are the prime numbers and e1,e2,... are nonnegative integers. Then a(n) = e1 + (e2)*4 + (e3)*16 + (e4)*64 + ... + (ek)*(4^(k-1)) + ...

0, 1, 4, 2, 16, 5, 64, 3, 8, 17, 256, 6, 1024, 65, 20, 4, 4096, 9, 16384, 18, 68, 257, 65536, 7, 32, 1025, 12, 66, 262144, 21, 1048576, 5, 260, 4097, 80, 10, 4194304, 16385, 1028, 19, 16777216, 69, 67108864, 258, 24, 65537, 268435456, 8, 128, 33, 4100, 1026

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OFFSET

1,3

COMMENTS

Replace "4" with "x" and extend the definition of a to positive rationals and a becomes an isomorphism between positive rationals under multiplication and polynomials over Z under addition. This remark generalizes A001222, A048675 and A054841: evaluate said polynomial at x=1, x=2 and x=10, respectively.

REFERENCES

Joseph J. Rotman, The Theory of Groups: An Introduction, 2nd ed. Boston: Allyn and Bacon, Inc. 1973. Page 9, problem 1.26.

LINKS

Table of n, a(n) for n=1..52.

Sam Alexander, {group theory} positive rationals under multiplication = polynomials under addition [post to sci.math].

CROSSREFS

Cf. A001222, A048675, A054841, A090880, A090882, A090883, A090884.

Sequence in context: A109922 A090640 A302213 * A191452 A348685 A110485

Adjacent sequences: A090878 A090879 A090880 * A090882 A090883 A090884

KEYWORD

easy,nonn

AUTHOR

Sam Alexander, Dec 12 2003

EXTENSIONS

More terms from Ray Chandler, Dec 20 2003

STATUS

approved