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A328168
Numbers whose prime indices minus 1 are relatively prime.
10
3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 35, 36, 39, 42, 45, 48, 51, 54, 57, 60, 63, 65, 66, 69, 70, 72, 75, 77, 78, 81, 84, 87, 90, 91, 93, 95, 96, 99, 102, 105, 108, 111, 114, 117, 120, 123, 126, 129, 130, 132, 133, 135, 138, 140, 141, 143, 144, 145, 147
OFFSET
1,1
COMMENTS
A multiset is relatively prime if the GCD of its elements is 1. Zeros are ignored when computing GCD, and the empty set has GCD 0.
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.
The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k), so these are Heinz numbers of partitions whose parts minus one are relatively prime. The enumeration of these partitions by sum is given by A328170.
EXAMPLE
The sequence of terms together with their prime indices begins:
3: {2}
6: {1,2}
9: {2,2}
12: {1,1,2}
15: {2,3}
18: {1,2,2}
21: {2,4}
24: {1,1,1,2}
27: {2,2,2}
30: {1,2,3}
33: {2,5}
35: {3,4}
36: {1,1,2,2}
39: {2,6}
42: {1,2,4}
45: {2,2,3}
48: {1,1,1,1,2}
51: {2,7}
54: {1,2,2,2}
57: {2,8}
MAPLE
q:= n-> igcd(map(i-> numtheory[pi](i[1])-1, ifactors(n)[2])[])=1:
select(q, [$1..150])[]; # Alois P. Heinz, Oct 13 2019
MATHEMATICA
Select[Range[100], GCD@@(PrimePi/@First/@If[#==1, {}, FactorInteger[#]]-1)==1&]
CROSSREFS
Positions of 1's in A328167.
Numbers whose prime indices are relatively prime are A289509.
The version for prime indices plus 1 is A318981.
The GCD of prime indices is A289508.
Partitions whose parts minus 1 are relatively prime are A328170.
Sequence in context: A212662 A342831 A161351 * A209258 A337244 A366847
KEYWORD
nonn
AUTHOR
Gus Wiseman, Oct 08 2019
STATUS
approved