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A354514
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Numbers k such that m - gpf(m) = k has solutions m >= 2, gpf = A006530.
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3
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0, 2, 3, 5, 6, 7, 9, 10, 11, 13, 14, 15, 17, 19, 20, 21, 22, 23, 24, 25, 26, 28, 29, 30, 31, 33, 34, 35, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 49, 51, 52, 53, 55, 56, 57, 58, 59, 61, 62, 63, 65, 66, 67, 68, 69, 70, 71, 73, 74, 75, 76, 77, 78, 79, 82, 83, 85, 86, 87, 88
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OFFSET
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1,2
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COMMENTS
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Numbers k such that there is a prime p such that gpf(k+p) = p (such p must be a prime factor of n).
Numbers k such that there is a prime factor p of k such that k+p is p-smooth.
A076563 sorted and duplicates removed.
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LINKS
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EXAMPLE
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0 is a term because 0 = p - gpf(p) for every prime p.
if k/gpf(k) <= nextprime(gpf(k)) - 2, where nextprime = A151800, then k is a term since k+gpf(k) <= gpf(k)*(nextprime(gpf(k)) - 1) implies gpf(k+gpf(k)) = gpf(k).
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PROG
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(PARI) gpf(n) = vecmax(factor(n)[, 1]);
isA354514(n) = if(n, my(f=factor(n)[, 1]); for(i=1, #f, if(gpf(n+f[i])==f[i], return(1))); 0, 1)
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CROSSREFS
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0 together with indices of positive terms in A354512. Complement of A354515.
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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