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A093891
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Numbers n such that every prime up to sigma(n) is a sum of divisors of n.
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5
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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; internal format)
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OFFSET
| 1,2
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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? - Frank Adams-Watters (FrankTAW(AT)Netscape.net), 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 (noe(AT)sspectra.com), Mar 19 2010]
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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.
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CROSSREFS
| Cf. A093890, A093892.
Cf. A005153.
Sequence in context: A114871 A085150 A051178 * A204010 A151999 A177917
Adjacent sequences: A093888 A093889 A093890 * A093892 A093893 A093894
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KEYWORD
| nonn
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AUTHOR
| Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Apr 23 2004
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EXTENSIONS
| More terms from Frank Adams-Watters (FrankTAW(AT)Netscape.net), Apr 28 2006
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