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 A118503 Sum of digits of prime factors of n, with multiplicity. 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; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS 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. LINKS G. C. Greubel, Table of n, a(n) for n = 0..5000 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. MAPLE A118503 := proc(n) local a; a := 0 ; for p in ifactors(n) do a := a+ op(2, p)*A007953(op(1, p)) ; end do: a ; end proc: # R. J. Mathar, Sep 14 2011 MATHEMATICA sdpf[n_]:=Total[Flatten[IntegerDigits/@Flatten[Table[#[], {#[]}]&/@FactorInteger[n]]]]; Join[{0, 0}, Array[sdpf, 100, 2]] (* Harvey P. Dale, Sep 19 2013 *) CROSSREFS Cf. A001221, A001222, A007953, A095402. Sequence in context: A081758 A106492 A112264 * A086295 A159303 A262049 Adjacent sequences:  A118500 A118501 A118502 * A118504 A118505 A118506 KEYWORD base,easy,nonn AUTHOR Jonathan Vos Post, May 06 2006 STATUS approved

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Last modified November 22 03:42 EST 2019. Contains 329388 sequences. (Running on oeis4.)