|
%I #14 Nov 12 2020 14:40:39
%S 125,275,425,575,605,775,935,1025,1175,1265,1331,1445,1475,1675,1705,
%T 1825,1955,2057,2075,2255,2425,2575,2585,2635,2645,2725,2783,3175,
%U 3179,3245,3425,3485,3565,3685,3725,3751,3925,3995,4015,4175,4301,4475,4565,4715
%N Products of three odd prime numbers of odd index.
%C Also Heinz numbers of integer partitions with 3 parts, all of which are odd and > 1. These partitions are counted by A001399.
%H Robert Israel, <a href="/A338469/b338469.txt">Table of n, a(n) for n = 1..10000</a>
%e The sequence of terms together with their prime indices begins:
%e 125: {3,3,3} 1825: {3,3,21} 3425: {3,3,33}
%e 275: {3,3,5} 1955: {3,7,9} 3485: {3,7,13}
%e 425: {3,3,7} 2057: {5,5,7} 3565: {3,9,11}
%e 575: {3,3,9} 2075: {3,3,23} 3685: {3,5,19}
%e 605: {3,5,5} 2255: {3,5,13} 3725: {3,3,35}
%e 775: {3,3,11} 2425: {3,3,25} 3751: {5,5,11}
%e 935: {3,5,7} 2575: {3,3,27} 3925: {3,3,37}
%e 1025: {3,3,13} 2585: {3,5,15} 3995: {3,7,15}
%e 1175: {3,3,15} 2635: {3,7,11} 4015: {3,5,21}
%e 1265: {3,5,9} 2645: {3,9,9} 4175: {3,3,39}
%e 1331: {5,5,5} 2725: {3,3,29} 4301: {5,7,9}
%e 1445: {3,7,7} 2783: {5,5,9} 4475: {3,3,41}
%e 1475: {3,3,17} 3175: {3,3,31} 4565: {3,5,23}
%e 1675: {3,3,19} 3179: {5,7,7} 4715: {3,9,13}
%e 1705: {3,5,11} 3245: {3,5,17} 4775: {3,3,43}
%p N:= 10000: # for terms <= N
%p P0:= [seq(ithprime(i),i=3..numtheory:-pi(floor(N/25)),2)]:
%p sort(select(`<=`,[seq(seq(seq(P0[i]*P0[j]*P0[k],k=1..j),j=1..i),i=1..nops(P0))], N)); # _Robert Israel_, Nov 12 2020
%t Select[Range[1,1000,2],PrimeOmega[#]==3&&OddQ[Times@@PrimePi/@First/@FactorInteger[#]]&]
%o (PARI) isok(m) = my(f=factor(m)); (m%2) && (bigomega(f)==3) && (#select(x->!(x%2), apply(primepi, f[,1]~)) == 0); \\ _Michel Marcus_, Nov 10 2020
%Y A046316 allows all primes (strict: A046389).
%Y A338471 allows all odd primes (strict: A307534).
%Y A338556 is the version for evens (strict: A338557).
%Y A000009 counts partitions into odd parts (strict: A000700).
%Y A001399(n-3) counts 3-part partitions (strict: A001399(n-6)).
%Y A005408 lists odds (strict: A056911).
%Y A008284 counts partitions by sum and length.
%Y A014311 is a ranking of 3-part compositions (strict: A337453).
%Y A014612 lists Heinz numbers of 3-part partitions (strict: A007304).
%Y A023023 counts 3-part relatively prime partitions (strict: A101271).
%Y A066207 lists numbers with all even prime indices (strict: A258117).
%Y A066208 lists numbers with all odd prime indices (strict: A258116).
%Y A075818 lists even Heinz numbers of 3-part partitions (strict: A075819).
%Y A285508 lists Heinz numbers of non-strict 3-part partitions.
%Y Cf. A001221, A001222, A002620, A005117, A037144, A056239, A112798.
%K nonn
%O 1,1
%A _Gus Wiseman_, Nov 08 2020
|
