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A093891 Numbers n such that every prime up to sigma(n) is a sum of divisors of n. 5
1, 2, 4, 6, 8, 10, 12, 16, 18, 20, 24, 28, 30, 32, 36, 40, 42, 48, 54, 56, 60, 64, 66, 70, 72, 78, 80, 84, 88, 90, 96, 100, 104, 108, 112, 120, 126, 128, 132, 140, 144, 150, 156, 160, 162, 168, 176, 180, 192, 196, 198, 200, 204, 208, 210, 216, 220, 224, 228, 234, 240 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Sequence is infinite as sigma (2^n)= 2^(n+1)-1 and a(2^n) = pi(2^(n+1)-1).

Does this sequence include any non-members of A005153 other than 10, 70 and 836? - Franklin T. Adams-Watters, Apr 28 2006

The answer to the previous comment is yes, this sequence has many terms that are not in A005153. See A174434. [From T. D. Noe, Mar 19 2010]

LINKS

Table of n, a(n) for n=1..61.

EXAMPLE

4 is a member as sigma(4) = 7 and all the primes up to 7 are a partial sum of divisors of 4.

Divisors of 4 are 1, 2 and 4 . Primes arising are 2, 3= 1+2, 5 = 1+4 and 7 = 1 + 2 + 4.

CROSSREFS

Cf. A093890, A093892.

Cf. A005153.

Sequence in context: A114871 A085150 A051178 * A213708 A239063 A151999

Adjacent sequences:  A093888 A093889 A093890 * A093892 A093893 A093894

KEYWORD

nonn

AUTHOR

Amarnath Murthy, Apr 23 2004

EXTENSIONS

More terms from Franklin T. Adams-Watters, Apr 28 2006

STATUS

approved

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Last modified March 31 03:08 EDT 2020. Contains 333136 sequences. (Running on oeis4.)