id:A078458 - OEIS Search Results

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

+0
6

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; listen)

	OFFSET	`1,2`
	LINKS	`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 (vladeta(AT)eunet.rs), 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 (noe(AT)sspectra.com), 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 (vladeta(AT)eunet.rs), 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: A104733 A153281 A130584 this_sequence A033317 A007733 A128520` `Adjacent sequences: A078455 A078456 A078457 this_sequence A078459 A078460 A078461`
	KEYWORD	`nonn,easy`
	AUTHOR	`N. J. A. Sloane (njas(AT)research.att.com), Jan 11 2003`
	EXTENSIONS	`More terms from Vladeta Jovovic (vladeta(AT)eunet.rs), Jan 12 2003`

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Last modified December 10 12:37 EST 2009. Contains 170569 sequences.

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