This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A338557 #17 Oct 18 2024 18:07:52
%S A338557 273,399,609,741,777,903,1113,1131,1281,1443,1491,1653,1659,1677,1729,
%T A338557 1869,2067,2109,2121,2247,2373,2379,2451,2639,2751,2769,2919,3021,
%U A338557 3081,3171,3219,3367,3423,3471,3477,3633,3741,3801,3857,3913,3939,4047,4053,4173
%N A338557 Products of three distinct prime numbers of even index.
%C A338557 All terms are odd.
%C A338557 Also sphenic numbers (A007304) with all even prime indices (A031215).
%C A338557 Also Heinz numbers of strict integer partitions with 3 parts, all of which are even. These partitions are counted by A001399.
%e A338557 The sequence of terms together with their prime indices begins:
%e A338557 273: {2,4,6} 1869: {2,4,24} 3219: {2,10,12}
%e A338557 399: {2,4,8} 2067: {2,6,16} 3367: {4,6,12}
%e A338557 609: {2,4,10} 2109: {2,8,12} 3423: {2,4,38}
%e A338557 741: {2,6,8} 2121: {2,4,26} 3471: {2,6,24}
%e A338557 777: {2,4,12} 2247: {2,4,28} 3477: {2,8,18}
%e A338557 903: {2,4,14} 2373: {2,4,30} 3633: {2,4,40}
%e A338557 1113: {2,4,16} 2379: {2,6,18} 3741: {2,10,14}
%e A338557 1131: {2,6,10} 2451: {2,8,14} 3801: {2,4,42}
%e A338557 1281: {2,4,18} 2639: {4,6,10} 3857: {4,8,10}
%e A338557 1443: {2,6,12} 2751: {2,4,32} 3913: {4,6,14}
%e A338557 1491: {2,4,20} 2769: {2,6,20} 3939: {2,6,26}
%e A338557 1653: {2,8,10} 2919: {2,4,34} 4047: {2,8,20}
%e A338557 1659: {2,4,22} 3021: {2,8,16} 4053: {2,4,44}
%e A338557 1677: {2,6,14} 3081: {2,6,22} 4173: {2,6,28}
%e A338557 1729: {4,6,8} 3171: {2,4,36} 4179: {2,4,46}
%t A338557 Select[Range[1000],SquareFreeQ[#]&&PrimeOmega[#]==3&&OddQ[Times@@(1+PrimePi/@First/@FactorInteger[#])]&]
%o A338557 (PARI) isok(m) = my(f=factor(m)); (bigomega(f)==3) && (omega(f)==3) && (#select(x->(x%2), apply(primepi, f[,1]~)) == 0); \\ _Michel Marcus_, Nov 10 2020
%o A338557 (Python)
%o A338557 from itertools import filterfalse
%o A338557 from math import isqrt
%o A338557 from sympy import primepi, primerange, nextprime, integer_nthroot
%o A338557 def A338557(n):
%o A338557 def bisection(f,kmin=0,kmax=1):
%o A338557 while f(kmax) > kmax: kmax <<= 1
%o A338557 while kmax-kmin > 1:
%o A338557 kmid = kmax+kmin>>1
%o A338557 if f(kmid) <= kmid:
%o A338557 kmax = kmid
%o A338557 else:
%o A338557 kmin = kmid
%o A338557 return kmax
%o A338557 def f(x): return int(n+x-sum((primepi(x//(k*m))>>1)-(b>>1) for a,k in filterfalse(lambda x:x[0]&1,enumerate(primerange(3,integer_nthroot(x,3)[0]+1),2)) for b,m in filterfalse(lambda x:x[0]&1,enumerate(primerange(nextprime(k)+1,isqrt(x//k)+1),a+2))))
%o A338557 return bisection(f,n,n) # _Chai Wah Wu_, Oct 18 2024
%Y A338557 For the following, NNS means "not necessarily strict".
%Y A338557 A007304 allows all prime indices (not just even) (NNS: A014612).
%Y A338557 A046389 allows all odd primes (NNS: A046316).
%Y A338557 A258117 allows products of any length (NNS: A066207).
%Y A338557 A307534 is the version for odds instead of evens (NNS: A338471).
%Y A338557 A337453 is a different ranking of ordered triples (NNS: A014311).
%Y A338557 A338556 is the NNS version.
%Y A338557 A001399(n-6) counts strict 3-part partitions (NNS: A001399(n-3)).
%Y A338557 A005117 lists squarefree numbers, with even case A039956.
%Y A338557 A078374 counts 3-part relatively prime strict partitions (NNS: A023023).
%Y A338557 A075819 lists even Heinz numbers of strict triples (NNS: A075818).
%Y A338557 A220377 counts 3-part pairwise coprime strict partitions (NNS: A307719).
%Y A338557 A258116 lists squarefree numbers with all odd prime indices (NNS: A066208).
%Y A338557 A285508 lists Heinz numbers of non-strict triples.
%Y A338557 Cf. A000217, A001221, A001222, A037144, A056239, A112798, A337605.
%K A338557 nonn
%O A338557 1,1
%A A338557 _Gus Wiseman_, Nov 08 2020