id:A118503 - OEIS Search Results

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Sum of digits of prime factors of n, with multiplicity.

+0
5

0, 0, 2, 3, 4, 5, 5, 7, 6, 6, 7, 2, 7, 4, 9, 8, 8, 8, 8, 10, 9, 10, 4, 5, 9, 10, 6, 9, 11, 11, 10, 4, 10, 5, 10, 12, 10, 10, 12, 7, 11, 5, 12, 7, 6, 11, 7, 11, 11, 14, 12, 11, 8, 8, 11, 7, 13, 13, 13, 14, 12, 7, 6, 13, 12, 9, 7, 13, 12, 8, 14, 8, 12, 10, 12, 13, 14, 9, 9, 16, 13 (list; graph; listen)

	OFFSET	`0,3`
	COMMENT	`This is to A095402 (Sum of digits of all distinct prime factors of n) as bigomega = A001222 is to omega = A001221. See also: A007953 Digital sum (i.e. sum of digits) of n.`
	FORMULA	`a(n) = SUM[i=1..k] (e_i)A007953(p_i) where prime decomposition of n = (p_1)^(e_1) (p_2)^(e_2) * ... * (p_k)^(e_k).`
	EXAMPLE	`a(22) = 4 because 22 = 2 * 11 and the digital sum of 2 + the digital sum of 11 = 2 + 2 = 4.` `a(121) = 4 because 121 = 11^2 = 11 * 11, summing the digits of the prime factors with multiplicity gives A007953(11) + A007953(11) = 2 + 2 = 4.` `a(1000) = 21 because = 2^3 * 5^3 = 2 * 2 * 2 * 5 * 5 * 5 and 2 + 2 + 2 + 5 + 5 + 5 = 21; as opposed to A095402(1000) = 7.`
	CROSSREFS	`Cf. A001221, A001222, A007953, A095402.` `Sequence in context: A029908 A081758 A106492 this_sequence A086295 A159303 A001414` `Adjacent sequences: A118500 A118501 A118502 this_sequence A118504 A118505 A118506`
	KEYWORD	`base,easy,nonn`
	AUTHOR	`Jonathan Vos Post (jvospost3(AT)gmail.com), May 06 2006`

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Last modified November 25 20:09 EST 2009. Contains 167514 sequences.

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