

A302591


One, powers of 2, and prime numbers of squarefree index.


1



1, 2, 3, 4, 5, 8, 11, 13, 16, 17, 29, 31, 32, 41, 43, 47, 59, 64, 67, 73, 79, 83, 101, 109, 113, 127, 128, 137, 139, 149, 157, 163, 167, 179, 181, 191, 199, 211, 233, 241, 256, 257, 269, 271, 277, 283, 293, 313, 317, 331, 347, 349, 353, 367, 373, 389, 397, 401
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OFFSET

1,2


COMMENTS

A prime index of n is a number m such that prime(m) divides n.


LINKS

Andrew Howroyd, Table of n, a(n) for n = 1..1000


FORMULA

Union of A000079 and A302491.  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 systems.
01: {}
02: {{}}
03: {{1}}
04: {{},{}}
05: {{2}}
08: {{},{},{}}
11: {{3}}
13: {{1,2}}
16: {{},{},{},{}}
17: {{4}}
29: {{1,3}}
31: {{5}}
32: {{},{},{},{},{}}
41: {{6}}
43: {{1,4}}
47: {{2,3}}
59: {{7}}
64: {{},{},{},{},{},{}}


MATHEMATICA

primeMS[n_]:=If[n===1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
Select[Range[400], Or[#===1, Union[primeMS[#]]==={1}, PrimeQ[#]&&SquareFreeQ[PrimePi[#]]]&]


PROG

(PARI) ok(n)={n>>valuation(n, 2) == 1  (isprime(n) && issquarefree(primepi(n)))} \\ Andrew Howroyd, Aug 26 2018


CROSSREFS

Cf. A000079, A000961, A001222, A003963, A005117, A007716, A056239, A275024, A279791, A281113, A296133, A301765, A302242, A302243, A302491.
Sequence in context: A093327 A186041 A322531 * A269571 A281493 A181341
Adjacent sequences: A302588 A302589 A302590 * A302592 A302593 A302594


KEYWORD

nonn


AUTHOR

Gus Wiseman, Apr 10 2018


STATUS

approved



