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 A322553 Odd numbers whose product of prime indices is a prime power. 1
 1, 3, 5, 7, 9, 11, 17, 19, 21, 23, 25, 27, 31, 41, 49, 53, 57, 59, 63, 67, 81, 83, 97, 103, 109, 115, 121, 125, 127, 131, 133, 147, 157, 159, 171, 179, 189, 191, 211, 227, 241, 243, 277, 283, 289, 311, 331, 343, 353, 361, 367, 371, 393, 399, 401, 419, 431, 441 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Differs from A322400 in having 1 and lacking 377, the MM-number of {{1,2},{1,3}}. A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798. LINKS EXAMPLE The multiset multisystem with MM-number n is formed by taking the multiset of prime indices of each part of the multiset of prime indices of n. For example, the prime indices of 78 are {1,2,6}, so the multiset multisystem with MM-number 78 is {{},{1},{1,2}}. The sequence of multiset partitions whose MM-numbers belong to this sequence begins:    1: {}    3: {{1}}    5: {{2}}    7: {{1,1}}    9: {{1},{1}}   11: {{3}}   17: {{4}}   19: {{1,1,1}}   21: {{1},{1,1}}   23: {{2,2}}   25: {{2},{2}}   27: {{1},{1},{1}}   31: {{5}}   41: {{6}}   49: {{1,1},{1,1}}   53: {{1,1,1,1}}   57: {{1},{1,1,1}}   59: {{7}}   63: {{1},{1},{1,1}}   67: {{8}}   81: {{1},{1},{1},{1}}   83: {{9}}   97: {{3,3}} MATHEMATICA primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]]; Select[Range[1, 100, 2], #==1||PrimePowerQ[Times@@primeMS[#]]&] PROG (PARI) isok(n) = {if (n % 2, my(f = factor(n), pk = prod(k=1, #f~, primepi(f[k, 1]))); (pk == 1) || isprimepower(pk); ); } \\ Michel Marcus, Dec 16 2018 CROSSREFS Cf. A003963, A056239, A112798, A290103, A302242, A320325, A320698. Sequence in context: A201644 A342949 A322400 * A302601 A064076 A050842 Adjacent sequences:  A322550 A322551 A322552 * A322554 A322555 A322556 KEYWORD nonn AUTHOR Gus Wiseman, Dec 15 2018 STATUS approved

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Last modified June 20 00:16 EDT 2021. Contains 345154 sequences. (Running on oeis4.)