A337471 Primorial inflation of n prime shifted once: a(n) = A003961(A108951(n)).

1, 3, 15, 9, 105, 45, 1155, 27, 225, 315, 15015, 135, 255255, 3465, 1575, 81, 4849845, 675, 111546435, 945, 17325, 45045, 3234846615, 405, 11025, 765765, 3375, 10395, 100280245065, 4725, 3710369067405, 243, 225225, 14549535, 121275, 2025, 152125131763605, 334639305, 3828825, 2835, 6541380665835015, 51975, 307444891294245705, 135135

Offset: 1

Author

Antti Karttunen, Aug 28 2020

Keywords

• nonn
• mult

Links

• Index entries for sequences computed from indices in prime factorization.
• Index entries for sequences related to primorial numbers.

Crossrefs

Row 1 of A337470.

Cf. A000265, A002110, A003961, A034386, A070826, A108951.

Programs

PARI

A003961(n) = my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f);
A034386(n) = prod(i=1, primepi(n), prime(i));
A108951(n) = { my(f=factor(n)); prod(i=1, #f~, A034386(f[i, 1])^f[i, 2]) }; \\ From A108951
A337471(n) = A003961(A108951(n));

Formula

a(n) = A003961(A108951(n)).

a(n) = A000265(A108951(A003961(n))).

Completely multiplicative with a(prime(i)) = A003961(A002110(i)) = A070826(1+i). - Antti Karttunen, Nov 17 2020

Sum_{n>=1} 1/a(n) = 1 / Product_{k>=2} (1 - 1/A070826(k)) = 1.6241170949... . - Amiram Eldar, Dec 08 2022