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 A054725 a(1)=1; a(n)= sum(p \ n, a(p-1)), where sum is over all primes p that divide n, with multiplicity. 2
 1, 1, 1, 2, 2, 2, 2, 3, 2, 3, 3, 3, 3, 3, 3, 4, 4, 3, 3, 4, 3, 4, 4, 4, 4, 4, 3, 4, 4, 4, 4, 5, 4, 5, 4, 4, 4, 4, 4, 5, 5, 4, 4, 5, 4, 5, 5, 5, 4, 5, 5, 5, 5, 4, 5, 5, 4, 5, 5, 5, 5, 5, 4, 6, 5, 5, 5, 6, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 4, 6, 6, 5, 6, 5, 5, 6, 6, 5, 5, 6, 5, 6, 5, 6, 6, 5, 5, 6, 6, 6, 6, 6 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 LINKS Joerg Arndt, Table of n, a(n) for n = 1..10000 FORMULA a(1) = 1 and a(n) = A064415(n) for n>=2. [Joerg Arndt, Apr 08 2014] EXAMPLE a(20) = a(2-1) + a(2-1) + a(5-1) = 1 + 1 +2 = 4 because 20 = 2*2*5. MATHEMATICA Fold[Append[#1, Total@ Table[#1[[p - 1]], {p, Flatten@ Map[ConstantArray[#1, #2] & @@ # &, FactorInteger[#2]]}]] &, {1}, Range[2, 105]] (* Michael De Vlieger, Dec 11 2017 *) PROG (PARI) a(n)=if (n<=1, 1, my(F=factor(n)); sum(e=1, #F[, 1], F[e, 2] * a(F[e, 1]-1) ) ); vector(200, n, a(n)) \\ Joerg Arndt, Apr 08 2014 CROSSREFS Sequence in context: A272314 A241216 A125173 * A064415 A086833 A010764 Adjacent sequences:  A054722 A054723 A054724 * A054726 A054727 A054728 KEYWORD nonn AUTHOR Leroy Quet, Apr 20 2000 STATUS approved

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Last modified February 18 04:48 EST 2020. Contains 332011 sequences. (Running on oeis4.)