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 A297365 Numbers k such that uphi(k)*usigma(k) = uphi(k+1)*usigma(k+1), where uphi is the unitary totient function (A047994) and usigma the sum of unitary divisors (A034448). 1
 5, 11, 19, 71, 247, 271, 991, 2232, 6200, 8271, 10295, 16744, 18496, 18576, 25704, 26656, 102175, 122607, 166624, 225939, 301103, 747967, 7237384, 7302592, 15760224, 21770800, 28121184, 72967087, 98617024, 104577848, 173859007, 253496176, 335610184, 371191600 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Equivalently, numbers k such that A191414(k) = A191414(k+1). - Amiram Eldar, Nov 09 2023 LINKS Amiram Eldar, Table of n, a(n) for n = 1..47 (terms below 10^11) EXAMPLE 11 is in the sequence since uphi(11) * usigma(11) = 10 * 12 = uphi(12) * usigma(12) = 6 * 20 = 120. MATHEMATICA usigma[n_] := If[n == 1, 1, Times @@ (1 + Power @@@ FactorInteger[n])]; uphi[n_] := (Times @@ (Table[#[[1]]^#[[2]] - 1, {1}] & /@ FactorInteger[n]))[[1]]; u[n_] := uphi[n]*usigma[n]; aQ[n_] := u[n] == u[n + 1]; Select[Range[10^6], aQ] PROG (PARI) A191414(n) = {my(f = factor(n)); prod(i = 1, #f~, f[i, 1]^(2*f[i, 2])-1); } lista(kmax) = {my(a1 = 1, a2); for(k = 2, kmax, a2 = A191414(k); if(a1 == a2, print1(k-1, ", ")); a1 = a2); } \\ Amiram Eldar, Nov 09 2023 CROSSREFS The unitary version of A244439. Cf. A034448, A047994, A191414. Sequence in context: A267603 A323007 A370682 * A128927 A145934 A033913 Adjacent sequences: A297362 A297363 A297364 * A297366 A297367 A297368 KEYWORD nonn AUTHOR Amiram Eldar, Dec 29 2017 STATUS approved

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Last modified May 21 04:01 EDT 2024. Contains 372720 sequences. (Running on oeis4.)