A297366 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).
6, 10, 12, 15, 18, 22, 24, 26, 28, 36, 40, 46, 48, 52, 58, 63, 72, 80, 82, 88, 96, 100, 106, 108, 112, 124, 136, 148, 162, 166, 172, 178, 192, 196, 226, 232, 242, 250, 262, 268, 285, 288, 292, 316, 346, 352, 358, 382, 388, 400, 432, 448, 466, 478, 486, 502
Offset: 1
Keywords
Examples
6 is in the sequence since uphi(6) + usigma(6) = 2 + 12 = uphi(7) + usigma(7) = 6 + 8 = 14.
Links
- Amiram Eldar, Table of n, a(n) for n = 1..10000
Programs
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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[10^3], aQ] -
PARI
u(k) = {my(f = factor(k)); prod(i = 1, #f~, f[i,1]^f[i,2]-1) + prod(i = 1, #f~, f[i,1]^f[i,2]+1);} list(kmax) = {my(u1 = u(1), u2); for(k = 2, kmax, u2 = u(k); if(u1 == u2, print1(k-1, ", ")); u1 = u2);} \\ Amiram Eldar, Jun 30 2025
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