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A327250
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Numbers k such that s(k) = s(k+1), where s(k) is A059975.
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1
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3, 80, 175, 272, 492, 860, 943, 6556, 6867, 7104, 7215, 14672, 17459, 21804, 22672, 24435, 24476, 26128, 30899, 34595, 39215, 41327, 45548, 49468, 56563, 57075, 63440, 63744, 67123, 72556, 78524, 87615, 90243, 104111, 109939, 113283, 113296, 115344, 121539, 131651
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OFFSET
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1,1
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COMMENTS
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Madeleine Farris named these numbers "Euler-totient Ruth-Aaron numbers" (in analogy to the Ruth-Aaron numbers, A039752). She proved that the number of terms <= x is O(x*(log(log(x))^4)/(log(x))^2) and that the sum of their reciprocals is bounded.
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LINKS
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EXAMPLE
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MATHEMATICA
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f[p_, e_] := e * (p-1); a[n_] := Plus @@ (f @@@ FactorInteger[n]); aQ[n_] := a[n] == a[n+1]; Select[Range[10^5], aQ]
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PROG
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(PARI) s(n) = {my(f = factor(n)); sum(i = 1, #f~, f[i, 2] * (f[i, 1] - 1)); }
lista(kmax) = {my(s1 = s(1), s2); for(k=2, kmax, s2 = s(k); if(s1 == s2, print1(k-1, ", ")); s1 = s2); } \\ Amiram Eldar, Apr 06 2023
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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