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A223548 Smallest prime factors for sequence A223546.

13, 229, 269, 331, 1036991, 193, 1187, 379, 942381313, 1078717, 1690920279179, 593, 181, 1433, 641, 139, 631, 2622013, 1123, 130337, 223, 155784593, 3746107, 1223, 13791824242727551, 67623587, 853, 299635177, 3966293, 197, 4755811387725362803, 263, 40637, 577

Offset: 1

Paul Larm, Mar 21 2013

nonn

			a(3) = 229, the smallest prime factor of A223546(3) = 233335657 = 229*307*3319.

Sean A. Irvine, Table of n, a(n) for n = 1..75 (terms 1..34 from Sidney Cadot)

Cf. A020639, A223546, A285528.

a(n) = A020639(A223546(n)).

a(n) = 463 for n >= 74. - Sean A. Irvine, Jul 20 2025

a(15)-a(34) from Chai Wah Wu, Oct 10 2019

A223546 Composite numbers in the sequence A217723.

Original entry on oeis.org

247, 233335657, 6703028887, 7628001653827, 311878265181037, 628284422185342477, 33217442899375387207, 1955977793053588026277, 119244359152460559009547, 7977565910232727614888637, 565918396036931688582304027, 3258940366335958863738288181627

Offset: 1

Paul Larm, Mar 21 2013

nonn

			a(1) = 247 = 13*19 which is the first composite number in sequence A217723.

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

Intersection of A002808 and A217723.

A217723 a(n) = (sum of first n primorial numbers) minus 1.

Original entry on oeis.org

1, 7, 37, 247, 2557, 32587, 543097, 10242787, 233335657, 6703028887, 207263519017, 7628001653827, 311878265181037, 13394639596851067, 628284422185342477, 33217442899375387207, 1955977793053588026277, 119244359152460559009547

Offset: 1

Paul Larm, Mar 21 2013

			For n = 4, a(4) = 2 + 2*3 + 2*3*5 + 2*3*5*7 - 1 = 247.

Paul Larm (terms 1..20) and Amiram Eldar (terms 21..100), Table of n, a(n) for n = 1..100
Paul Larm, Table of a(n) for n = 2..25 showing prime factors.

Equals A060389 - 1. Cf. A223546, A223548.

Accumulate[Denominator[Accumulate[1/Prime[Range[20]]]]] - 1 (* Alonso del Arte, Mar 21 2013 *)
Accumulate[Table[Fold[Times,Prime[Range[n]]],{n,20}]]-1 (* Harvey P. Dale, May 23 2020 *)

a(1) = P(1)# - 1, a(2) = P(1)# + P(2)# -1; where P(n)# is the product of first n prime numbers (primorial#).

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User: Paul Larm

A223548 Smallest prime factors for sequence A223546.

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A223546 Composite numbers in the sequence A217723.

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A217723 a(n) = (sum of first n primorial numbers) minus 1.

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