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 A339113 #12 Mar 17 2021 08:02:00
%S A339113 1,13,29,43,47,73,79,101,137,139,149,163,167,169,199,233,257,269,271,
%T A339113 293,313,347,373,377,389,421,439,443,449,467,487,491,499,559,577,607,
%U A339113 611,631,647,653,673,677,727,751,757,811,821,823,829,839,841,907,929,937
%N A339113 Products of primes of squarefree semiprime index (A322551).
%C A339113 A squarefree semiprime (A006881) is a product of any two distinct prime numbers.
%C A339113 Also MM-numbers of labeled multigraphs (without uncovered vertices). A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798. The multiset of multisets with MM-number n is formed by taking the multiset of prime indices of each part of the multiset of prime indices of n. For example, the prime indices of 78 are {1,2,6}, so the multiset of multisets with MM-number 78 is {{},{1},{1,2}}.
%e A339113 The sequence of terms together with the corresponding multigraphs begins:
%e A339113 1: {} 233: {{2,7}} 487: {{2,11}}
%e A339113 13: {{1,2}} 257: {{3,5}} 491: {{1,15}}
%e A339113 29: {{1,3}} 269: {{2,8}} 499: {{3,8}}
%e A339113 43: {{1,4}} 271: {{1,10}} 559: {{1,2},{1,4}}
%e A339113 47: {{2,3}} 293: {{1,11}} 577: {{1,16}}
%e A339113 73: {{2,4}} 313: {{3,6}} 607: {{2,12}}
%e A339113 79: {{1,5}} 347: {{2,9}} 611: {{1,2},{2,3}}
%e A339113 101: {{1,6}} 373: {{1,12}} 631: {{3,9}}
%e A339113 137: {{2,5}} 377: {{1,2},{1,3}} 647: {{1,17}}
%e A339113 139: {{1,7}} 389: {{4,5}} 653: {{4,7}}
%e A339113 149: {{3,4}} 421: {{1,13}} 673: {{1,18}}
%e A339113 163: {{1,8}} 439: {{3,7}} 677: {{2,13}}
%e A339113 167: {{2,6}} 443: {{1,14}} 727: {{2,14}}
%e A339113 169: {{1,2},{1,2}} 449: {{2,10}} 751: {{4,8}}
%e A339113 199: {{1,9}} 467: {{4,6}} 757: {{1,19}}
%t A339113 sqfsemiQ[n_]:=SquareFreeQ[n]&&PrimeOmega[n]==2;
%t A339113 Select[Range[1000],FreeQ[If[#==1,{},FactorInteger[#]],{p_,k_}/;!sqfsemiQ[PrimePi[p]]]&]
%Y A339113 These primes (of squarefree semiprime index) are listed by A322551.
%Y A339113 The strict (squarefree) case is A309356.
%Y A339113 The prime instead of squarefree semiprime version:
%Y A339113 primes: A006450
%Y A339113 products: A076610
%Y A339113 strict: A302590
%Y A339113 The nonprime instead of squarefree semiprime version:
%Y A339113 primes: A007821
%Y A339113 products: A320628
%Y A339113 odd: A320629
%Y A339113 strict: A340104
%Y A339113 odd strict: A340105
%Y A339113 The semiprime instead of squarefree semiprime version:
%Y A339113 primes: A106349
%Y A339113 products: A339112
%Y A339113 strict: A340020
%Y A339113 A001358 lists semiprimes, with odd/even terms A046315/A100484.
%Y A339113 A002100 counts partitions into squarefree semiprimes.
%Y A339113 A005117 lists squarefree numbers.
%Y A339113 A006881 lists squarefree semiprimes, with odd/even terms A046388/A100484.
%Y A339113 A056239 gives the sum of prime indices, which are listed by A112798.
%Y A339113 A302242 is the weight of the multiset of multisets with MM-number n.
%Y A339113 A305079 is the number of connected components for MM-number n.
%Y A339113 A320911 lists products of squarefree semiprimes (Heinz numbers of A338914).
%Y A339113 A338899/A270650/A270652 give the prime indices of squarefree semiprimes.
%Y A339113 A339561 lists products of distinct squarefree semiprimes (ranking: A339560).
%Y A339113 MM-numbers: A255397 (normal), A302478 (set multisystems), A320630 (set multipartitions), A302494 (sets of sets), A305078 (connected), A316476 (antichains), A318991 (chains), A320456 (covers), A328514 (connected sets of sets), A329559 (clutters), A340019 (half-loop graphs).
%Y A339113 Cf. A000040, A000720, A001055, A001222, A003963, A289509, A320461.
%K A339113 nonn
%O A339113 1,2
%A A339113 _Gus Wiseman_, Mar 12 2021