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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. 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

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

LINKS

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

EXAMPLE

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.

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

PROG

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

CROSSREFS

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

Sequence in context: A230379 A292847 A088270 * A338525 A267586 A224507

Adjacent sequences: A259493 A259494 A259495 * A259497 A259498 A259499

KEYWORD

nonn

AUTHOR

Paolo P. Lava, Jun 29 2015

EXTENSIONS

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

STATUS

approved

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Last modified January 27 12:24 EST 2023. Contains 359840 sequences. (Running on oeis4.)