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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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified December 8 03:17 EST 2021. Contains 349590 sequences. (Running on oeis4.)