A063740 -id:A063740 - cp's OEIS frontend

A072073 Number of solutions to cototient(x) = A051953(x) = 2^n.

1, 2, 3, 3, 4, 4, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 10

Offset: 1

Labos Elemer, Jun 13 2002

nonn

a(n) increases at A000043(n).

Since A051953(p) = 1 for p prime, and given that there are an infinite number of primes, we disregard a(0) = oo. - Michael De Vlieger, Mar 25 2020

			InvCototient(2^0) has an infinite number of entries, so 2^0=1 is left out.
n=14: 2^14=16384, InvCototient(16384) = {24576,28672,31744,32512,32764,32768}, so a(14)=6;

Cf. A051953, A058764, A000043, A063740, A000079.

Length /@ Most@ Split@ DeleteCases[Select[Array[# - EulerPhi[#] &, 10^6], IntegerQ@ Log2@ # &], 1] (* Michael De Vlieger, Mar 25 2020 *)

a(n) = A063740(A000079(n)). - Ridouane Oudra, Jun 02 2024

A072297 Number of even non-cototients not exceeding 2^n.

Original entry on oeis.org

0, 0, 0, 1, 2, 6, 10, 23, 48, 99, 194, 392, 791, 1600, 3290, 6810, 13900, 28269, 57455, 116213, 234237, 470861, 945510, 1897007, 3802257, 7616206, 15244011, 30493702, 60965480, 121838430, 243409121, 486131077, 970680425, 1937876841, 3868346975

Offset: 1

Robert G. Wilson v, Jul 13 2002 and Jul 29 2002

			a(6) = 6 because the even non-cototients not exceeding 64 are {10,26,34,50,52,58}.

Number of terms in A063740 <= 2^n. Cf. A072077.

a = Table[0, {2^26}]; Do[ b = n - EulerPhi[n]; If[ EvenQ[b] && b < 2^27 + 1, a[[b/2]]++ ], {n, 2, 10^9}]; c = 0; k = 1; Do[While[k < 2^n, If[a[[k]] == 0, c++ ]; k++ ]; Print[c], {n, 1, 26}]

a(16) and a(21) corrected and a(28)-a(32) from Donovan Johnson, Jun 23 2010

a(33)-a(35) from Donovan Johnson, Jun 03 2013

cp's OEIS Frontend

A072073 Number of solutions to cototient(x) = A051953(x) = 2^n.

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