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A279068 Smallest prime of the form 1 + p + p^2 + p^3 + ... + p^k, where p is the n-th prime. 1
3, 13, 31, 2801, 50544702849929377, 30941, 307, 109912203092239643840221, 292561, 732541, 917087137, 6765811783780036261, 1723, 3500201 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Equivalently, smallest prime of the form (p^(k+1)-1)/(p-1), where p is the n-th prime.

For p prime, the sum of divisors of p^k is Sum_{j=0..k} p^j, so a(n) is the smallest prime of the form sigma(prime(n)^k) where sigma is the sum of divisors function A000203.

For the corresponding values of k, see A279069.

a(15) = 1 + 47 + 47^2 + ... + 47^126 = 4.93935...*10^210.

a(57) > 10^10000.

LINKS

Table of n, a(n) for n=1..14.

CROSSREFS

Cf. A000203, A279069.

Sequence in context: A073337 A128067 A052493 * A247216 A301926 A211800

Adjacent sequences:  A279065 A279066 A279067 * A279069 A279070 A279071

KEYWORD

nonn

AUTHOR

Jon E. Schoenfield, Dec 22 2016; edited Dec 23 2016

STATUS

approved

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Last modified May 30 05:08 EDT 2020. Contains 334712 sequences. (Running on oeis4.)