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A302569 Numbers that are either prime or whose prime indices are pairwise coprime. Heinz numbers of integer partitions with pairwise coprime parts. 76
2, 3, 4, 5, 6, 7, 8, 10, 11, 12, 13, 14, 15, 16, 17, 19, 20, 22, 23, 24, 26, 28, 29, 30, 31, 32, 33, 34, 35, 37, 38, 40, 41, 43, 44, 46, 47, 48, 51, 52, 53, 55, 56, 58, 59, 60, 61, 62, 64, 66, 67, 68, 69, 70, 71, 73, 74, 76, 77, 79, 80, 82, 83, 85, 86, 88, 89 (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 Heinz number of an integer partition (y_1,..,y_k) is prime(y_1)*..*prime(y_k).
LINKS
Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
EXAMPLE
Entry A302242 describes a correspondence between positive integers and multiset multisystems. In this case it gives the following sequence of multiset systems.
02: {{}}
03: {{1}}
04: {{},{}}
05: {{2}}
06: {{},{1}}
07: {{1,1}}
08: {{},{},{}}
10: {{},{2}}
11: {{3}}
12: {{},{},{1}}
13: {{1,2}}
14: {{},{1,1}}
15: {{1},{2}}
16: {{},{},{},{}}
17: {{4}}
19: {{1,1,1}}
20: {{},{},{2}}
22: {{},{3}}
23: {{2,2}}
24: {{},{},{},{1}}
26: {{},{1,2}}
28: {{},{},{1,1}}
29: {{1,3}}
30: {{},{1},{2}}
31: {{5}}
32: {{},{},{},{},{}}
MATHEMATICA
primeMS[n_]:=If[n===1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
Select[Range[200], Or[PrimeQ[#], CoprimeQ@@primeMS[#]]&]
PROG
(PARI) is(n)=if(n<9, return(n>1)); n>>=valuation(n, 2); if(n<9, return(1)); my(f=factor(n)); if(vecmax(f[, 2])>1, return(0)); if(#f~==1, return(1)); my(v=apply(primepi, f[, 1]), P=vecprod(v)); for(i=1, #v, if(gcd(v[i], P/v[i])>1, return(0))); 1 \\ Charles R Greathouse IV, Nov 11 2021
CROSSREFS
Subsequence of A122132.
Sequence in context: A020662 A306202 A328335 * A235034 A331682 A107037
KEYWORD
nonn
AUTHOR
Gus Wiseman, Apr 10 2018
STATUS
approved

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Last modified March 28 12:26 EDT 2024. Contains 371254 sequences. (Running on oeis4.)