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A302592
One, powers of 2, and prime numbers of prime index.
1
1, 2, 3, 4, 5, 8, 11, 16, 17, 31, 32, 41, 59, 64, 67, 83, 109, 127, 128, 157, 179, 191, 211, 241, 256, 277, 283, 331, 353, 367, 401, 431, 461, 509, 512, 547, 563, 587, 599, 617, 709, 739, 773, 797, 859, 877, 919, 967, 991, 1024, 1031, 1063, 1087, 1153, 1171
OFFSET
1,2
LINKS
FORMULA
Union of A000079 and A006450. - Andrew Howroyd, Aug 26 2018
EXAMPLE
Entry A302242 describes a correspondence between positive integers and multiset multisystems. In this case it gives the following sequence of set multisystems.
001: {}
002: {{}}
003: {{1}}
004: {{},{}}
005: {{2}}
008: {{},{},{}}
011: {{3}}
016: {{},{},{},{}}
017: {{4}}
031: {{5}}
032: {{},{},{},{},{}}
041: {{6}}
059: {{7}}
064: {{},{},{},{},{},{}}
067: {{8}}
083: {{9}}
109: {{10}}
127: {{11}}
128: {{},{},{},{},{},{},{}}
MATHEMATICA
primeMS[n_]:=If[n===1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
Select[Range[1000], Or[#===1, Union[primeMS[#]]==={1}, PrimeQ[#]&&PrimeQ[PrimePi[#]]]&]
PROG
(PARI) ok(n)={n>>valuation(n, 2) == 1 || (isprime(n) && isprime(primepi(n)))} \\ Andrew Howroyd, Aug 26 2018
KEYWORD
nonn
AUTHOR
Gus Wiseman, Apr 10 2018
STATUS
approved