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 A237524 Number of ordered ways to write n = i + j + k with 0 < i <= j <= k such that phi(i*j*k) is a cube, where phi(.) is Euler's totient function. 2
 0, 0, 1, 1, 0, 0, 0, 1, 4, 3, 2, 2, 1, 1, 1, 1, 2, 5, 2, 3, 2, 3, 6, 5, 4, 4, 4, 5, 4, 5, 4, 6, 6, 5, 5, 9, 6, 10, 8, 7, 7, 5, 5, 4, 11, 10, 8, 10, 5, 8, 8, 10, 10, 8, 11, 16, 11, 13, 14, 16, 18, 19, 18, 16, 24, 19, 21, 18, 15, 21, 9, 15, 14, 13, 15, 18, 19, 20, 15, 19 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,9 COMMENTS Conjecture: For each k = 3, 4, ..., any integer n > 2*k + 1 can be written as a sum of k positive integers n_1, n_2, ..., n_k such that phi(n_1*n_2*...*n_k) is a k-th power. Note that 2*k + 2 = (k-1)*2 + 4 with phi(2^(k-1)*4) = 2^k. See also A237523 for a similar conjecture with k = 2. LINKS Zhi-Wei Sun, Table of n, a(n) for n = 1..1500 EXAMPLE a(4) = 1 since 4 = 1 + 1 + 2 with phi(1*1*2) = 1^3. a(13) = 1 since 13 = 1 + 2 + 10 with phi(1*2*10) = 2^3. a(16) = 1 since 16 = 4 + 4 + 8 with phi(4*4*8) = phi(2^7) = 4^3. MATHEMATICA CQ[n_]:=IntegerQ[n^(1/3)] q[n_]:=CQ[EulerPhi[n]] a[n_]:=Sum[If[q[i*j(n-i-j)], 1, 0], {i, 1, n/3}, {j, i, (n-i)/2}] Table[a[n], {n, 1, 80}] CROSSREFS Cf. A000010, A000578, A233386, A237050, A237123, A237523. Sequence in context: A108438 A347738 A082504 * A266143 A171623 A117462 Adjacent sequences:  A237521 A237522 A237523 * A237525 A237526 A237527 KEYWORD nonn AUTHOR Zhi-Wei Sun, Feb 09 2014 STATUS approved

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Last modified July 7 12:08 EDT 2022. Contains 355148 sequences. (Running on oeis4.)