A378746 a(n) = Product{i=n..primepi(2*prime(n))} prime(i).

6, 15, 35, 1001, 46189, 96577, 6678671, 14535931, 1348781387, 146078888479, 18128893780549, 203079283326684719, 433601713048867373, 877779077635511999, 1816798556036292277, 39006703653387621491281, 969956148531489825059765363, 16439934720872708899318057, 4483790064773102589474664169, 1274400211992152128527851190601

Offset

1,1

Comments

Each a(n) is a proper divisor of A007741(n).

Each a(n) or one of its proper divisors is present in A337372.

a(n) is the least product of consecutive primes starting from A000040(n) such that A003961(a(n)) > 2*a(n). Note that 6, 15, 35, 46189 and 96577 are all present in A337372, i.e., are primitively primeshift-abundant numbers. For 1001 = 7*11*31, it is however its proper divisor 91 = 7*31 which gets that honor.

Links

Antti Karttunen, Table of n, a(n) for n = 1..344

Prog

(PARI) A378746(n) = prod(i=n, primepi(2*prime(n)), prime(i));

Crossrefs

Cf. A003961, A007741, A063124 [= A001222(a(n))], A337372.

Subsequence of A097889.

Cf. also A378745.

Sequence in context: A099620 A045969 A100513 * A338057 A191002 A127469

Adjacent sequences: A378743 A378744 A378745 * A378747 A378748 A378749

Keyword

nonn

Author

Antti Karttunen, Dec 08 2024

Status

approved