A078458 - OEIS

This site is supported by donations to The OEIS Foundation.

A078458

Total number of factors in a factorization of n into Gaussian primes.

0, 2, 1, 4, 2, 3, 1, 6, 2, 4, 1, 5, 2, 3, 3, 8, 2, 4, 1, 6, 2, 3, 1, 7, 4, 4, 3, 5, 2, 5, 1, 10, 2, 4, 3, 6, 2, 3, 3, 8, 2, 4, 1, 5, 4, 3, 1, 9, 2, 6, 3, 6, 2, 5, 3, 7, 2, 4, 1, 7, 2, 3, 3, 12, 4, 4, 1, 6, 2, 5, 1, 8, 2, 4, 5, 5, 2, 5, 1, 10, 4, 4, 1, 6, 4, 3, 3, 7, 2, 6, 3, 5, 2, 3, 3, 11, 2, 4, 3, 8, 2, 5, 1, 8 (list; graph; refs; listen; history; text; internal format)

	OFFSET	`1,2`
	COMMENTS	`a(n)+1 is also the total number of factors in a factorization of n+n*i into Gaussian primes. - Jason Kimberley, Dec 17 2011`
	LINKS	`Table of n, a(n) for n=1..104.` `Michael Somos, PARI program for finding prime decomposition of Gaussian integers` `Index entries for Gaussian integers and primes` `Eric Weisstein's World of Mathematics, Gaussian Prime`
	FORMULA	`Fully additive with a(p)=2 if p=2 or p mod 4=1 and a(p)=1 if p mod 4=3. - Vladeta Jovovic, Jan 20 2003` `a(n) depends on the number of primes of the forms 4k+1 (A083025) and 4k-1 (A065339) and on the highest power of 2 dividing n (A007814): a(n) = 2A007814(n) + 2A083025(n) + A065339(n) - T. D. Noe, Jul 14 2003`
	EXAMPLE	`2 = (1+i)(1-i), so a(2) = 2; 9 = 33, so a(9) = 2.` `a(1006655265000) = a(2^33^25^47^511^3) = 3a(2)+2a(3)+4a(5)+5a(7)+3a(11) = 32+21+42+51+31 = 24. - Vladeta Jovovic, Jan 20 2003`
	CROSSREFS	`Cf. A078908-A078911.` `Cf. A007814, A065339, A083025, A086275 (number of distinct Gaussian primes in the factorization of n).` `Sequence in context: A201703 A153281 A130584 * A033317 A183200 A007733` `Adjacent sequences: A078455 A078456 A078457 * A078459 A078460 A078461`
	KEYWORD	`nonn,easy`
	AUTHOR	`N. J. A. Sloane, Jan 11 2003`
	EXTENSIONS	`More terms from Vladeta Jovovic, Jan 12 2003`
	STATUS	`approved`

Content is available under The OEIS End-User License Agreement .

Last modified May 25 12:15 EDT 2013. Contains 225647 sequences.