A051272 - OEIS

A051272

Number of numbers neither relatively prime to nor divisors of primorial number(n).

0, 1, 15, 147, 1799, 24207, 418223, 8040555, 186596999, 5447822127, 169904385683, 6317118444315, 260105476063019, 11228680258501647, 529602053223466643, 28154196550210395195, 1665532558389396635999

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OFFSET

1,3

LINKS

Michael De Vlieger, Table of n, a(n) for n = 1..349

FORMULA

a(n) = A045763(A002110(n)).

a(n) = primorial(n) - (phi(primorial(n)) + tau(primorial(n)) - 1). - Michael De Vlieger, Feb 04 2015

EXAMPLE

The 4th primorial (210) has 16 divisors and 48 coprimes, so a(4) = 210 - 64 + 1 = 147.

MATHEMATICA

# - (EulerPhi@ # + DivisorSigma[0, #] - 1) & /@ (Product[ Prime@ i, {i, 1, #}] & /@ Range@ 17) (* Michael De Vlieger, Feb 04 2015 *)

PROG

(PARI) a002110(n) = prod(i=1, n, prime(i));

a(n) = my(pr = a002110(n)); pr - numdiv(pr) - eulerphi(pr) + 1; \\ Michel Marcus, Feb 22 2015

CROSSREFS

Cf. A000005, A000010, A002110, A045763, A051271.

Sequence in context: A245755 A240419 A069417 * A021414 A211847 A055431

Adjacent sequences: A051269 A051270 A051271 * A051273 A051274 A051275

KEYWORD

nonn

AUTHOR

Labos Elemer

STATUS

approved