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Search: id:A157973
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| A157973 |
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Numbers n > 1 with spf(n) < n such that there is a number k, n < k <= 2*n, with k - spf(k) = n - spf(n). |
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2
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| 9, 12, 20, 21, 24, 25, 28, 35, 40, 44, 49, 52, 54, 55, 56, 57, 63, 65, 72, 77, 81, 88, 90, 91, 92, 93, 95, 96, 98, 105, 108, 111, 115, 116, 119, 121, 125, 126, 128, 130, 133, 143, 144, 145, 147, 148, 150, 155, 161, 164, 165, 169, 170, 172, 180, 184, 185, 187, 188, 189
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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spf(k) is the sum of the prime factors of k with multiplicity, cf. A001414.
Condition spf(n) < n excludes 4 and the primes.
It appears that if a number k > n with k - spf(k) = n - spf(n) exists at all, then k <= 2*n. If this can be proved, the corresponding condition in the definition could be omitted.
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EXAMPLE
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For n = 77, n-spf(n) = 77-18 = 59; for k = 93, k-spf(k) = 93-34 =59. Hence 77 is in the sequence.
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PROGRAM
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(MAGMA) spf:=func< n | &+[a[1]*a[2]: a in Factorization(n)] >; [ n: n in [2..190] | d gt 0 and exists(t){ k: k in [n+1..2*n] | d eq k-spf(k) } where d is n-spf(n) ];
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CROSSREFS
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Cf. A001414 (sum of primes dividing n).
Sequence in context: A087269 A153973 A072702 this_sequence A057577 A014766 A114434
Adjacent sequences: A157970 A157971 A157972 this_sequence A157974 A157975 A157976
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KEYWORD
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nonn
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AUTHOR
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J. M. Bergot (thekingfishb(AT)yahoo.ca), Mar 10 2009
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EXTENSIONS
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Edited, missing terms inserted and extended by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Mar 30 2009
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