A385743 Numbers k such that A384247(k) = A384247(k+1).

1, 20, 27, 35, 63, 64, 104, 143, 194, 208, 740, 836, 1220, 1299, 1419, 1803, 1892, 2625, 3255, 3705, 3716, 3843, 4096, 5184, 5186, 5635, 5695, 7868, 10659, 13365, 16904, 17948, 18507, 18914, 21007, 22935, 25388, 25545, 27675, 30380, 31599, 32304, 32864, 34595

Offset: 1

Author

Amiram Eldar, Jul 08 2025

Keywords

• nonn

Comments

63 is the only number k below 10^11 such that A384247(k) = A384247(k+1) = A384247(k+2). Are there any other such terms?

Examples

			1 is a term since A384247(1) = A384247(2) = 1.
20 is a term since A384247(20) = A384247(21) = 12.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..4006 (terms below 10^11)

Crossrefs

Cf. A384247.

Similar sequences: A001274, A287055, A293184, A301866, A326403, A349307.

Programs

Mathematica

f[p_, e_] := p^e*(1 - 1/p^(2^(IntegerExponent[e, 2]))); iphi[1] = 1; iphi[n_] := iphi[n] = Times @@ f @@@ FactorInteger[n]; Select[Range[35000], iphi[#] == iphi[# + 1] &]

PARI

iphi(n) = {my(f = factor(n)); n * prod(i = 1, #f~, (1 - 1/f[i, 1]^(1 << valuation(f[i, 2], 2)))); }
list(lim) = {my(s1 = iphi(1), s2); for(k = 2, lim, s2 = iphi(k); if(s1 == s2, print1(k-1, ", ")); s1 = s2);}