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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.)