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A302796
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Squarefree numbers whose prime indices are relatively prime. Nonprime Heinz numbers of strict integer partitions with relatively prime parts.
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35
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1, 2, 6, 10, 14, 15, 22, 26, 30, 33, 34, 35, 38, 42, 46, 51, 55, 58, 62, 66, 69, 70, 74, 77, 78, 82, 85, 86, 93, 94, 95, 102, 105, 106, 110, 114, 118, 119, 122, 123, 130, 134, 138, 141, 142, 143, 145, 146, 154, 155, 158, 161, 165, 166, 170, 174, 177, 178, 182
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OFFSET
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1,2
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COMMENTS
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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.
The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k).
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LINKS
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EXAMPLE
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Sequence of terms together with their sets of prime indices begins:
01 : {}
02 : {1}
06 : {1,2}
10 : {1,3}
14 : {1,4}
15 : {2,3}
22 : {1,5}
26 : {1,6}
30 : {1,2,3}
33 : {2,5}
34 : {1,7}
35 : {3,4}
38 : {1,8}
42 : {1,2,4}
46 : {1,9}
51 : {2,7}
55 : {3,5}
58 : {1,10}
62 : {1,11}
66 : {1,2,5}
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MATHEMATICA
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Select[Range[100], Or[#===1, SquareFreeQ[#]&&GCD@@PrimePi/@FactorInteger[#][[All, 1]]===1]&]
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PROG
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(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
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CROSSREFS
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Cf. A001222, A003963, A005117, A007359, A051424, A056239, A275024, A289509, A302242, A302505, A302696, A302697, A302698, A302797, A302798.
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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