|
|
A342010
|
|
Number of times the term 2 has occurred so far in the range 1..n of A073751.
|
|
4
|
|
|
1, 1, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,3
|
|
COMMENTS
|
Number of prime factors (with multiplicity) in the primorial deflation of the n-th colossally abundant number [A342012(n) = A319626(A004490(n))], provided that the quotient A004490(1+n)/A004490(n) is always a prime.
|
|
LINKS
|
|
|
FORMULA
|
a(n) = Sum_{k=1..n} [2==A073751(k)], where [ ] is the Iverson bracket.
|
|
MATHEMATICA
|
Block[{a = {2}, b, c, f, k, m, n, q = {1}, lim = 105}, f[w_] := Block[{p = w[[1]], i = w[[2]]}, ((Log[(p^(i + 2) - 1)/(p^(i + 1) - 1)])/Log[p]) - 1]; m = {{2, 1}, {3, 0}}; c = 1; b = Array[f[m[[#]]] &, c + 1]; For[n = 2, n <= lim, n++, k = Position[b, Max[b]][[1, 1]]; AppendTo[a, m[[k, 1]]]; AppendTo[q, Boole[m[[k, 1]] == 2]]; m[[k, 2]]++; If[k > c, c++; AppendTo[m, {Prime[k + 1], 0}]; AppendTo[b, f[m[[-1]]]]]; b[[k]] = f[m[[k]]]]; Accumulate@ q] (* Michael De Vlieger, Mar 12 2021, after T. D. Noe at A073751 *)
|
|
PROG
|
(PARI)
v073751 = readvec("b073751_to.txt"); \\ Prepared with gawk '{ print $2 }' < b073751.txt > b073751_to.txt
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|