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A353393
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Positive integers m > 1 that are prime or whose prime shadow A181819(m) is a divisor of m that is already in the sequence.
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13
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2, 3, 5, 7, 9, 11, 13, 17, 19, 23, 29, 31, 36, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 125, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 225, 227, 229, 233, 239, 241, 251
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OFFSET
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1,1
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COMMENTS
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We define the prime shadow A181819(n) to be the product of primes indexed by the exponents in the prime factorization of n. For example, 90 = prime(1)*prime(2)^2*prime(3) has prime shadow prime(1)*prime(2)*prime(1) = 12.
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LINKS
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FORMULA
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EXAMPLE
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The terms together with their prime indices begin:
2: {1}
3: {2}
5: {3}
7: {4}
9: {2,2}
11: {5}
13: {6}
17: {7}
19: {8}
23: {9}
29: {10}
31: {11}
36: {1,1,2,2}
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MATHEMATICA
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red[n_]:=If[n==1, 1, Times@@Prime/@Last/@FactorInteger[n]];
suQ[n_]:=PrimeQ[n]||Divisible[n, red[n]]&&suQ[red[n]];
Select[Range[2, 200], suQ[#]&]
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CROSSREFS
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The first term that is not a prime power A000961 is 36.
The first term that is not a perfect power A001597 is 1260.
These partitions are counted by A353426.
The version for compositions is A353431.
A003963 gives product of prime indices.
A130091 lists numbers with all distinct prime exponents, counted by A098859.
A325131 lists numbers relatively prime to their prime shadow.
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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