

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
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OFFSET

1,3


COMMENTS

Number of prime factors (with multiplicity) in the primorial deflation of the nth colossally abundant number [A342012(n) = A319626(A004490(n))], provided that the quotient A004490(1+n)/A004490(n) is always a prime.


LINKS

Table of n, a(n) for n=1..98.


FORMULA

a(n) = Sum_{k=1..n} [2==A073751(k)], where [ ] is the Iverson bracket.
a(n) = A001222(A342012(n)) = A000120(A342013(n)).


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
A073751(n) = v073751[n];
A342010(n) = sum(k=1, n, (2==A073751(k)));


CROSSREFS

Cf. A000120, A001222, A004490, A073751, A319626, A342012, A342013.
Sequence in context: A087828 A330779 A110867 * A006670 A132914 A060646
Adjacent sequences: A342007 A342008 A342009 * A342011 A342012 A342013


KEYWORD

nonn


AUTHOR

Antti Karttunen, Mar 08 2021


STATUS

approved



