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 A330946 Odd numbers whose prime indices are not all prime numbers. 7
 7, 13, 19, 21, 23, 29, 35, 37, 39, 43, 47, 49, 53, 57, 61, 63, 65, 69, 71, 73, 77, 79, 87, 89, 91, 95, 97, 101, 103, 105, 107, 111, 113, 115, 117, 119, 129, 131, 133, 137, 139, 141, 143, 145, 147, 149, 151, 159, 161, 163, 167, 169, 171, 173, 175, 181, 183, 185 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS 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. Also MM-numbers of multiset partitions whose parts not all singletons (see example). LINKS Table of n, a(n) for n=1..58. EXAMPLE The sequence of terms together with their prime indices of prime indices begins: 7: {{1,1}} 13: {{1,2}} 19: {{1,1,1}} 21: {{1},{1,1}} 23: {{2,2}} 29: {{1,3}} 35: {{2},{1,1}} 37: {{1,1,2}} 39: {{1},{1,2}} 43: {{1,4}} 47: {{2,3}} 49: {{1,1},{1,1}} 53: {{1,1,1,1}} 57: {{1},{1,1,1}} 61: {{1,2,2}} 63: {{1},{1},{1,1}} 65: {{2},{1,2}} 69: {{1},{2,2}} 71: {{1,1,3}} 73: {{2,4}} MATHEMATICA Select[Range[1, 100, 2], !And@@PrimeQ/@PrimePi/@First/@If[#==1, {}, FactorInteger[#]]&] CROSSREFS Odd numbers n such that A330944(n) > 0. Including even numbers gives A330945. The restriction to nonprimes is A330949. Taking nonprimes instead of odds gives A330947. The number of prime prime indices is given by A257994. Primes of prime index are A006450. Primes of nonprime index are A007821. Products of primes of prime index are A076610. Products of primes of nonprime index are A320628. The set S of numbers whose prime indices do not all belong to S is A324694. Cf. A000040, A000720, A001222, A018252, A056239, A112798, A302242, A320629, A330943, A330947, A330948. Sequence in context: A173928 A304995 A339657 * A160007 A024613 A024606 Adjacent sequences: A330943 A330944 A330945 * A330947 A330948 A330949 KEYWORD nonn AUTHOR Gus Wiseman, Jan 13 2020 STATUS approved

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Last modified June 6 05:06 EDT 2023. Contains 363139 sequences. (Running on oeis4.)