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

1, 2, 4, 6, 8, 10, 12, 14, 16, 20, 24, 28, 40, 56, 60, 80, 84, 104, 112, 120, 144, 160, 168, 184, 200, 208, 216, 224, 240, 260, 288, 320, 360, 368, 400, 416, 432, 460, 480, 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

Offset: 1

Author

Antti Karttunen, Dec 28 2019

Keywords

• nonn

Links

• Amiram Eldar, Table of n, a(n) for n = 1..1004 (calculated using the b-file at A330687; terms 1..285 from Antti Karttunen)

Crossrefs

Cf. A050376, A050377, A330687.

Programs

PARI

upto_e = 101; \\ 101 --> 211 terms
A018819(n) = if( n<1, n==0, if( n%2, A018819(n-1), A018819(n/2)+A018819(n-1))); \\ From A018819
v018819 = vector(upto_e,n,A018819(n));
A050377(n) = factorback(apply(e -> v018819[e], factor(n)[, 2]));
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
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); };
v330688 = A330688list(upto_e);
A330688(n) = v330688[n];

Formula

a(n) = A050377(A330687(n)).