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 A380316 #13 Jan 21 2025 11:49:13
%S A380316 385,555,759,897,935,957,1185,1245,1265,1335,2015,2037,2185,2211,2261,
%T A380316 2379,2607,2821,2877,2937,3059,3298,3363,3434,3485,3507,3538,3815,
%U A380316 3913,4029,4255,4378,4433,4526,4615,4738,4795,4947,5181,5205,5395,5405,5523,5681,5829,5883,6226
%N A380316 Sphenic numbers that are the sum of two successive sphenics.
%C A380316 The sum of two consecutive sphenic numbers varies as 4n log n/(log log n)^2, so this sequence is not smaller than that. - _Charles R Greathouse IV_, Jan 21 2025
%H A380316 Charles R Greathouse IV, <a href="/A380316/b380316.txt">Table of n, a(n) for n = 1..10000</a>
%e A380316 385 = 5*7*11 is a member because 385 = 190+195, sum of 18-th and 19-th sphenic number.
%e A380316 555 = 3*5*37 is a member because 555 = 273+292, sum of 28-th and 29-th sphenic number.
%p A380316 issphenic:= proc(n) local F; F:= ifactors(n)[2]; F[..,2] = [1,1,1] end proc:
%p A380316 S:= select(issphenic, [$1..10000]):
%p A380316 select(issphenic, S[1..-2]+S[2..-1]);
%p A380316 # _Robert Israel_, Jan 20 2025
%t A380316 sphenicQ[n_] := FactorInteger[n][[;; , 2]] == {1, 1, 1}; Select[MovingMap[Total, Select[Range[3200], sphenicQ], 1], sphenicQ] (* _Amiram Eldar_, Jan 21 2025 *)
%o A380316 (PARI) issphenic(n) = my(f=factor(n)); (bigomega(f)==3) && (omega(f)==3);
%o A380316 lista(nn) = my(v=select(issphenic, [1..nn])); select(issphenic, vector(#v-1, k, v[k]+v[k+1])); \\ _Michel Marcus_, Jan 20 2025
%o A380316 (PARI) sphen(lim)=my(v=List(), t); forprime(p=2, sqrtnint(lim\=1,3), forprime(q=p+1, sqrtint(lim\p), t=p*q; forprime(r=q+1, lim\t, listput(v, t*r)))); Set(v)
%o A380316 has(n,f=factor(n))=f[,2]==[1,1,1]~
%o A380316 list(lim)=my(v=List(),u=sphen(lim\2)); for(i=2,#u, if(has(u[i]+u[i-1]), listput(v,u[i]+u[i-1]))); forfactored(k=lim\2+1,lim\1-u[#u], if(has(0,k[2]), if(has(k[1]+u[#u]), listput(v,k[1]+u[#u])); break)); Vec(v) \\ _Charles R Greathouse IV_, Jan 21 2025
%Y A380316 Cf. A001043, A007304, A092192.
%K A380316 nonn
%O A380316 1,1
%A A380316 _Massimo Kofler_, Jan 20 2025