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 A177349 #11 Sep 13 2019 08:04:30
%S A177349 2,5,13,17,29,37,43,59,61,83,103,107,139,151,157,163,167,179,199,211,
%T A177349 223,227,233,241,251,257,269,283,307,313,317,331,347,373,379,409,419,
%U A177349 433,443,457,503,509,523,541,547,563,569,571,587,601,607,617,619,643
%N A177349 Primes p for which no m! has a prime power factorization of the form 2^p*...*p^1*...
%C A177349 One can prove that for p>=5 the number of such m is 0 or 2.
%H A177349 Amiram Eldar, <a href="/A177349/b177349.txt">Table of n, a(n) for n = 1..10000</a>
%H A177349 Vladimir Shevelev, <a href="http://dx.doi.org/10.4064/aa126-3-1">Compact integers and factorials</a>, Acta Arithmetica 126 (2007) 195-236.
%e A177349 p=109 is not in the sequence because for m=112 we have 112! = 2^109*3^54*...*109 which is of the form 2^p*...*p*.. [_R. J. Mathar_, Oct 29 2010]
%p A177349 isA177349 := proc(p) if isprime(p) then pid := numtheory[pi](p) ; for m from 1 do h2 := A115627(m,1) ; if h2 > p then return true; elif h2 = p then if A115627(m,pid) = 1 then return false; end if; end if; end do; else false; fi ; end proc:
%p A177349 for i from 1 to 120 do p := ithprime(i) ; if isA177349(p) then printf("%d,",p); end if; end do: # _R. J. Mathar_, Oct 29 2010
%t A177349 c[n_, p_] := Sum[IntegerExponent[k, p], {k, 2, n}]; m = 120; v = Table[0, {m}]; s = 0; n = 2; While[s <= Prime[m], s += IntegerExponent[n, 2]; If[ PrimeQ[s] && (i = PrimePi[s]) <= m && c[n, s] == 1, v[[i]] = 1]; n++]; t = Prime /@ (Position[v, _?(# == 0 &)] // Flatten); t (* _Amiram Eldar_, Sep 13 2019 *)
%Y A177349 Cf. A000142.
%K A177349 nonn
%O A177349 1,1
%A A177349 _Vladimir Shevelev_, May 07 2010
%E A177349 2 added, 109 replaced by 107, sequence extended beyond 199 by _R. J. Mathar_, Oct 29 2010