A298761 - OEIS

%I #18 Nov 18 2018 13:12:55

%S 2,20,35,40,44,215,235,245,2611,23319,26288,65113,174647,318544,

%T 1301317,1302509,1919376,3719225,5021647,10885081,36319939,49172608,

%U 70112131,70113559,325575773,514258883,742327529,1069238453

%N Numbers n such that n = pi(n) + uphi(n), where pi = A000720, uphi = A047994.

%C The unitary version of A037170.

%e 20 is in the sequence since pi(20) + uphi(20) = 8 + 12 = 20.

%t uphi[n_] := (Times @@ (Table[#[[1]]^#[[2]] - 1, {1}] & /@ FactorInteger[n]))[[1]]; seqQ[n_] := (n - uphi[n] == PrimePi[n]); Select[Range[10^7], seqQ]

%o (PARI) uphi(n) = my(f=factor(n)); prod(k=1, #f~, f[k, 1]^f[k, 2]-1);

%o isok(n) = n == primepi(n) + uphi(n); \\ _Michel Marcus_, Feb 13 2018

%Y Cf. A000720, A037170, A047994.

%K nonn,more

%O 1,1

%A _Amiram Eldar_, Jan 26 2018

%E a(20)-a(22) from _Daniel Suteu_, Mar 28 2018

%E a(23)-a(28) from _Daniel Suteu_, Nov 18 2018