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 A255242 Calculate the aliquot parts of a number n and take their sum. Then repeat the process calculating the aliquot parts of all the previous aliquot parts and add their sum to the previous one. Repeat the process until the sum to be added is zero. Sequence lists these sums. 3
 0, 1, 1, 4, 1, 8, 1, 12, 5, 10, 1, 30, 1, 12, 11, 32, 1, 36, 1, 38, 13, 16, 1, 92, 7, 18, 19, 46, 1, 74, 1, 80, 17, 22, 15, 140, 1, 24, 19, 116, 1, 90, 1, 62, 51, 28, 1, 256, 9, 62, 23, 70, 1, 136, 19, 140, 25, 34, 1, 286, 1, 36, 61, 192, 21, 122, 1, 86, 29, 114 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS a(n) = 1 if n is prime. LINKS Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Paolo P. Lava) FORMULA a(1) = 0. a(2^k) = k*2^(k-1) = A001787(k), for k>=1. a(n^k) = (n^k-2^k))/(n-2), for n odd prime and k>=1. In particular: a(3^k)  = A001047(k-1); a(5^k)  = A016127(k-1); a(7^k)  = A016130(k-1); a(11^k) = A016135(k-1). EXAMPLE The aliquot parts of 8 are 1, 2, 4 and their sum is 7. Now, let us calculate the aliquot parts of 1, 2 and 4: 1 => 0;  2 => 1;  4 => 1, 2.  Their sum is 0 + 1 + 1 + 2 = 4. Let us calculate the aliquot parts of 1, 1, 2: 1 => 0;  1 = > 0; 2 => 1. Their sum is 1. We have left 1: 1 => 0. Finally, 7 + 4 + 1 = 12. Therefore a(8) = 12. MAPLE with(numtheory): P:=proc(q) local a, b, c, k, n, t, v; for n from 1 to q do b:=0; a:=sort([op(divisors(n))]); t:=nops(a)-1; while add(a[k], k=1..t)>0 do b:=b+add(a[k], k=1..t); v:=[]; for k from 2 to t do c:=sort([op(divisors(a[k]))]); v:=[op(v), op(c[1..nops(c)-1])]; od; a:=v; t:=nops(a); od; print(b); od; end: P(10^3); MATHEMATICA f[s_] := Flatten[Most[Divisors[#]] & /@ s]; a[n_] := Total@Flatten[FixedPointList[ f, {n}]] - n; Array[a, 100] (* Amiram Eldar, Apr 06 2019 *) CROSSREFS Cf. A001047, A001065, A001787, A006516, A016127, A016130, A016135, A255243. Sequence in context: A158496 A265722 A019425 * A329371 A305834 A295786 Adjacent sequences:  A255239 A255240 A255241 * A255243 A255244 A255245 KEYWORD nonn AUTHOR Paolo P. Lava, Feb 19 2015 STATUS approved

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Last modified November 28 07:52 EST 2021. Contains 349401 sequences. (Running on oeis4.)