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%I #7 Apr 13 2018 21:54:39
%S 1,2,6,10,14,15,22,26,30,33,34,35,38,42,46,51,55,58,62,66,69,70,74,77,
%T 78,82,85,86,93,94,95,102,105,106,110,114,118,119,122,123,130,134,138,
%U 141,142,143,145,146,154,155,158,161,165,166,170,174,177,178,182
%N Squarefree numbers whose prime indices are relatively prime. Nonprime Heinz numbers of strict integer partitions with relatively prime parts.
%C A prime index of n is a number m such that prime(m) divides n. Two or more numbers are relatively prime if they have no common divisor other than 1. A single number is not considered relatively prime unless it is equal to 1.
%C The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k).
%e Sequence of terms together with their sets of prime indices begins:
%e 01 : {}
%e 02 : {1}
%e 06 : {1,2}
%e 10 : {1,3}
%e 14 : {1,4}
%e 15 : {2,3}
%e 22 : {1,5}
%e 26 : {1,6}
%e 30 : {1,2,3}
%e 33 : {2,5}
%e 34 : {1,7}
%e 35 : {3,4}
%e 38 : {1,8}
%e 42 : {1,2,4}
%e 46 : {1,9}
%e 51 : {2,7}
%e 55 : {3,5}
%e 58 : {1,10}
%e 62 : {1,11}
%e 66 : {1,2,5}
%t Select[Range[100],Or[#===1,SquareFreeQ[#]&&GCD@@PrimePi/@FactorInteger[#][[All,1]]===1]&]
%o (PARI) isok(n) = {if (n == 1, return (1)); if (issquarefree(n), my(f = factor(n)); return (gcd(vector(#f~, k, primepi(f[k,1]))) == 1););} \\ _Michel Marcus_, Apr 13 2018
%Y Cf. A001222, A003963, A005117, A007359, A051424, A056239, A275024, A289509, A302242, A302505, A302696, A302697, A302698, A302797, A302798.
%K nonn
%O 1,2
%A _Gus Wiseman_, Apr 13 2018
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