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A330688 Record values in A050377, number of ways to factor n into "Fermi-Dirac primes" (A050376).

%I A330688 #12 Apr 11 2025 03:26:20
%S A330688 1,2,4,6,8,10,12,14,16,20,24,28,40,56,60,80,84,104,112,120,144,160,
%T A330688 168,184,200,208,216,224,240,260,288,320,360,368,400,416,432,460,480,
%U A330688 520,576,600,624,640,720,736,800,864,920,960,1040,1104,1120,1152,1200,1440,1456,1472,1480,1600,1840,2016,2080,2400,2576,2880,2960,3360
%N A330688 Record values in A050377, number of ways to factor n into "Fermi-Dirac primes" (A050376).
%H A330688 Amiram Eldar, <a href="/A330688/b330688.txt">Table of n, a(n) for n = 1..1004</a> (calculated using the b-file at A330687; terms 1..285 from Antti Karttunen)
%F A330688 a(n) = A050377(A330687(n)).
%o A330688 (PARI)
%o A330688 upto_e = 101; \\ 101 --> 211 terms
%o A330688 A018819(n) = if( n<1, n==0, if( n%2, A018819(n-1), A018819(n/2)+A018819(n-1))); \\ From A018819
%o A330688 v018819 = vector(upto_e,n,A018819(n));
%o A330688 A050377(n) = factorback(apply(e -> v018819[e], factor(n)[, 2]));
%o A330688 A283980(n) = {my(f=factor(n)); prod(i=1, #f~, my(p=f[i, 1], e=f[i, 2]); if(p==2, 6, nextprime(p+1))^e)}; \\ From A283980
%o A330688 A330688list(e) = { my(lista = List([1, 2]), i=2, u = 2^e, t, m=0, v025487); while(lista[i] != u, if(2*lista[i] <= u, listput(lista,2*lista[i]); t = A283980(lista[i]); if(t <= u, listput(lista,t))); i++); v025487 = vecsort(Vec(lista)); lista = List([]); for(i=1,#v025487,if((t=A050377(v025487[i]))>m, listput(lista,t); m=t)); Vec(lista); };
%o A330688 v330688 = A330688list(upto_e);
%o A330688 A330688(n) = v330688[n];
%Y A330688 Cf. A050376, A050377, A330687.
%K A330688 nonn
%O A330688 1,2
%A A330688 _Antti Karttunen_, Dec 28 2019