A301866 -id:A301866 - cp's OEIS frontend

A326403 Numbers k such that iphi(k) = iphi(k+1), where iphi(k) is an infinitary analog to the Euler totient function (A091732).

1, 20, 35, 143, 194, 208, 740, 1220, 1299, 1419, 1803, 1892, 3705, 3716, 3843, 5186, 5635, 7868, 10659, 13634, 13905, 17948, 18507, 18914, 18980, 21007, 25388, 25545, 30380, 31599, 32304, 34595, 37820, 47067, 70394, 73059, 78064, 87856, 94874, 105908, 116963

Offset: 1

Amiram Eldar, Sep 14 2019

nonn

			20 is in the sequence since iphi(20) = iphi(21) = 12.

Amiram Eldar, Table of n, a(n) for n = 1..1000

Cf. A001274, A091732, A287055, A293184, A301866.

f[p_, e_] := p^(2^(-1 + Position[Reverse @ IntegerDigits[e, 2], ?(# == 1 &)])); a[1] = 1; a[n] := Times @@ (Flatten @(f @@@ FactorInteger[n]) - 1); a1 = 1; s = {}; Do[a2 = a[n]; If[a1 == a2, AppendTo[s, n - 1]]; a1 = a2, {n, 2, 10^5}]; s

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

Original entry on oeis.org

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

Amiram Eldar, Jul 08 2025

nonn

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?

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

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

Cf. A384247.

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

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] &]

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);}

cp's OEIS Frontend

A326403 Numbers k such that iphi(k) = iphi(k+1), where iphi(k) is an infinitary analog to the Euler totient function (A091732).

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Mathematica