cp's OEIS Frontend

A338552 Non-powers of primes whose prime indices have a common divisor > 1.

%I A338552 #13 Jan 09 2021 00:51:48
%S A338552 21,39,57,63,65,87,91,111,115,117,129,133,147,159,171,183,185,189,203,
%T A338552 213,235,237,247,259,261,267,273,299,301,303,305,319,321,325,333,339,
%U A338552 351,365,371,377,387,393,399,417,427,441,445,453,477,481,489,497,507
%N A338552 Non-powers of primes whose prime indices have a common divisor > 1.
%C A338552 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.
%C A338552 Also Heinz numbers of non-constant, non-relatively prime partitions. The Heinz number of a partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k), giving a bijective correspondence between positive integers and integer partitions.
%F A338552 Equals A024619 /\ A318978.
%F A338552 Complement of A000961 \/ A289509.
%e A338552 The sequence of terms together with their prime indices begins:
%e A338552      21: {2,4}      183: {2,18}       305: {3,18}
%e A338552      39: {2,6}      185: {3,12}       319: {5,10}
%e A338552      57: {2,8}      189: {2,2,2,4}    321: {2,28}
%e A338552      63: {2,2,4}    203: {4,10}       325: {3,3,6}
%e A338552      65: {3,6}      213: {2,20}       333: {2,2,12}
%e A338552      87: {2,10}     235: {3,15}       339: {2,30}
%e A338552      91: {4,6}      237: {2,22}       351: {2,2,2,6}
%e A338552     111: {2,12}     247: {6,8}        365: {3,21}
%e A338552     115: {3,9}      259: {4,12}       371: {4,16}
%e A338552     117: {2,2,6}    261: {2,2,10}     377: {6,10}
%e A338552     129: {2,14}     267: {2,24}       387: {2,2,14}
%e A338552     133: {4,8}      273: {2,4,6}      393: {2,32}
%e A338552     147: {2,4,4}    299: {6,9}        399: {2,4,8}
%e A338552     159: {2,16}     301: {4,14}       417: {2,34}
%e A338552     171: {2,2,8}    303: {2,26}       427: {4,18}
%t A338552 Select[Range[100],!(#==1||PrimePowerQ[#]||GCD@@PrimePi/@First/@FactorInteger[#]==1)&]
%Y A338552 A318978 allows prime powers, counted by A018783, with complement A289509.
%Y A338552 A327685 allows nonprime prime powers.
%Y A338552 A338330 is the coprime instead of relatively prime version.
%Y A338552 A338554 counts the partitions with these Heinz numbers.
%Y A338552 A338555 is the complement.
%Y A338552 A000740 counts relatively prime compositions.
%Y A338552 A000961 lists powers of primes, with complement A024619.
%Y A338552 A051424 counts pairwise coprime or singleton partitions.
%Y A338552 A108572 counts nontrivial periodic partitions, with Heinz numbers A001597.
%Y A338552 A291166 ranks relatively prime compositions, with complement A291165.
%Y A338552 A302696 gives the Heinz numbers of pairwise coprime partitions.
%Y A338552 A327516 counts pairwise coprime partitions, with Heinz numbers A302696.
%Y A338552 Cf. A000005, A000837, A007916, A056239, A112798, A289508, A302569, A302796, A318716, A327658, A328867, A328677, A338331, A338553.
%K A338552 nonn
%O A338552 1,1
%A A338552 _Gus Wiseman_, Nov 03 2020