A259496 Numbers n such that phi(n) + d(n) = phi(n+1) + d(n+1), where phi(n) is the Euler totient function of n and d(n) the number of divisors of n.

5, 7, 104, 105, 1754, 3255, 16215, 22935, 67431, 93074, 983775, 1025504, 2200694, 2619705, 3365438, 4163355, 4447064, 4695704, 6372794, 7838265, 9718904, 11903775, 23992215, 26879684, 29357475, 37239735, 40588485, 41207144, 48615735, 56424555, 76466985, 81591194, 83864055

Offset: 1

Author

Paolo P. Lava, Jun 29 2015

Keywords

• nonn

Comments

So far, less than 10^9, except for 7, 67431 & 3365438, all terms have been congruent to 5 or 4 (mod 10). - Robert G. Wilson v, Jul 06 2015

Examples

			phi(5) + d(5) = 4 + 2 = 6 and phi(6) + d(6) = 2 + 4 = 6.
phi(7) + d(7) = 6 + 2 = 8 and phi(8) + d(8) = 4 + 4 = 8.
		

Links

• Giovanni Resta, Table of n, a(n) for n = 1..600 (first 65 terms from Robert G. Wilson v)

Crossrefs

Cf. A000005, A000010, A061468, A054004, A145749, A259495.

Programs

Magma

[n: n in [1..6*10^6] | EulerPhi(n) + NumberOfDivisors(n) eq EulerPhi(n+1) + NumberOfDivisors(n+1)]; // Vincenzo Librandi, Jun 30 2015

Maple

with(numtheory): P:=proc(q) local n; for n from 1 to q do
if phi(n)+tau(n)=phi(n+1)+tau(n+1) then print(n); fi;
od; end: P(10^9);

Mathematica

a = k = 2; lst = {}; While[k < 100000001, b = EulerPhi[k] + DivisorSigma[0, k]; If[a == b, AppendTo[lst, k - 1]]; k++; a = b]; lst

Extensions

a(23)-a(33) from Robert G. Wilson v, Jul 05 2015