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 A002098 G.f.: 1/Product_{k>=1} (1-prime(k)*x^prime(k)). (Formerly M0597 N0215) 7
 1, 0, 2, 3, 4, 11, 17, 29, 49, 85, 144, 226, 404, 603, 1025, 1679, 2558, 4201, 6677, 10190, 16599, 25681, 39643, 61830, 96771, 147114, 228338, 352725, 533291, 818624, 1263259, 1885918, 2900270, 4396577, 6595481, 10040029, 15166064, 22642064 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS a(n) is sum of all numbers k for which A001414(k), the sum of prime factors with repetition, equals n.  See Havermann's link. - J. M. Bergot, Jun 14 2013 REFERENCES S.M. Kerawala, On a Pair of Arithmetic Functions Analogous to Chawla's Pair, J. Natural Sciences and Mathematics, 9 (1969), circa p. 103. N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence). N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS T. D. Noe, Table of n, a(n) for n=0..500 MAPLE b:= proc(n, i) option remember;       if n<0 then 0     elif n=0 then 1     elif i=0 then 0     else b(n, i-1) +b(n-ithprime(i), i) *ithprime(i)       fi     end: a:= n-> b(n, numtheory[pi](n)): seq(a(n), n=0..40);  # Alois P. Heinz, Nov 20 2010 MATHEMATICA b[n_, i_] := b[n, i] = Which[n<0, 0, n==0, 1, i==0, 0, True, b[n, i-1] + b[n - Prime[i], i]*Prime[i]]; a[n_] := b[n, PrimePi[n]]; Table[a[n], {n, 0, 40}] (* Jean-François Alcover, Feb 19 2016, after Alois P. Heinz *) CROSSREFS Cf. A002099. Row sums of A064364, A116864. Sequence in context: A061919 A328883 A192613 * A301318 A297180 A162969 Adjacent sequences:  A002095 A002096 A002097 * A002099 A002100 A002101 KEYWORD nonn AUTHOR EXTENSIONS Better description and more terms from Vladeta Jovovic, May 09 2003 STATUS approved

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Last modified September 18 16:55 EDT 2020. Contains 337170 sequences. (Running on oeis4.)