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
KEYWORD
nonn
AUTHOR
Gus Wiseman, Apr 10 2018
STATUS
approved