A070820 Difference between n-th prime and the value of commutator[phi,gpf] = commutator[A000010, A006530] at the same prime argument.

2, 3, 3, 4, 6, 4, 3, 4, 12, 8, 6, 4, 6, 8, 24, 14, 30, 6, 12, 8, 4, 14, 42, 12, 4, 6, 18, 54, 4, 8, 8, 14, 18, 24, 38, 6, 14, 4, 84, 44, 90, 6, 20, 4, 8, 12, 8, 38, 114, 20, 30, 18, 6, 6, 3, 132, 68, 6, 24, 8, 48, 74, 18, 32, 14, 80, 12, 8, 174, 30, 12, 180, 62, 32, 8, 192, 98, 12, 6, 18

Offset

1,1

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Formula

a(n) = A000040(n) - A070812(A000040(n)) = prime(n) - A070819(n); odd differences (=3) appear only at Fermat primes, i.e., at prime indices of n = {2, 3, 7, 55, 6543}. a(1) = 2 - 0 by convention.

Example

For n=100: prime(100) = 541, phi(541) = 540, gpf(540) = 5, gpf(541) = 541, phi(541) = 540, A070819(100) = 535, a(100) = A070820(100) = 541 - 535.

Mathematica

pf[x_] := Part[Reverse[Flatten[FactorInteger[x]]], 2] f[x_] := EulerPhi[pf[x]]-pf[EulerPhi[x]] Table[Prime[w]-f[Prime[w]], {w, 2, 128}]

Prog

(PARI) a(n)=if(n>1, my(f=factor(prime(n)-1)[, 1]); f[#f]+1, 2)

Crossrefs

Cf. A000010, A000040, A006530, A070812, A070813, A070819.

Sequence in context: A278288 A023154 A358073 * A234360 A317838 A213938

Adjacent sequences: A070817 A070818 A070819 * A070821 A070822 A070823

Keyword

nonn

Author

Labos Elemer, May 10 2002

Status

approved