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A086469
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Sum of the distinct (smallest) prime signature divisors of n. In case of two or more divisors with the same prime signature the smallest is considered to evaluate the sum. Let this function be defined as psigma(n).
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2
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1, 3, 4, 7, 6, 9, 8, 15, 13, 13, 12, 25, 14, 17, 19, 31, 18, 36, 20, 37, 25, 25, 24, 57, 31, 29, 40, 49, 30, 39, 32, 63, 37, 37, 41, 61, 38, 41, 43, 85, 42, 51, 44, 73, 73, 49, 48, 121, 57, 88, 55, 85, 54, 117, 61, 113, 61, 61, 60, 115, 62, 65, 97, 127, 71, 75, 68, 109, 73, 83, 72
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Define n as a 'psigma perfect number' if psigma(n) = 2n. 18 is a psigma perfect number. The p sigma divisors are 1,2,6,9 and 18 and the sum = 36. Conjecture: 18 is the only psigma perfect number.
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EXAMPLE
| a(30) = 1 + 2 + 6 + 30 = 39. The divisors 3, 5,10 and 15 are not considered for the sum as 3 and 5 have the same prime signature as 2 and also 10 and 15 have the same prime signature as 6.
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CROSSREFS
| Cf. A086470.
Sequence in context: A204823 A096842 A147966 * A087030 A175187 A126253
Adjacent sequences: A086466 A086467 A086468 * A086470 A086471 A086472
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KEYWORD
| nonn
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AUTHOR
| Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Jul 21 2003
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EXTENSIONS
| More terms from David Wasserman (wasserma(AT)spawar.navy.mil), Mar 07 2005
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