

A177329


Number of factors in the representation of n! as a product of distinct terms of A050376.


8



1, 2, 3, 4, 3, 4, 6, 6, 4, 5, 7, 8, 9, 10, 11, 12, 8, 9, 9, 11, 12, 13, 13, 14, 15, 16, 14, 15, 16, 17, 19, 21, 17, 16, 15, 16, 17, 18, 19, 20, 22, 23, 21, 21, 21, 22, 23, 22, 23, 25, 22, 23, 22, 24, 26, 28, 28, 29, 27, 28, 29, 30, 32, 34, 30, 31, 31, 28, 27, 28, 29, 30, 31, 33, 31, 31, 30
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

2,2


REFERENCES

V. S. Shevelev, Multiplicative functions in the FermiDirac arithmetic, Izvestia Vuzov of the NorthCaucasus region, Nature sciences 4 (1996), 2843 [Russian].


LINKS

Amiram Eldar, Table of n, a(n) for n = 2..1000
Simon Litsyn and Vladimir Shevelev, On factorization of integers with restrictions on the exponent, INTEGERS: Electronic Journal of Combinatorial Number Theory, 7 (2007), #A33, 136.


FORMULA

a(n) = sum A000120(e_i), where n! = product p_i^e_i is the prime factorization of n!.
a(n) = A064547(n!). [R. J. Mathar, May 28 2010]


MAPLE

read("transforms") ; A064547 := proc(n) f := ifactors(n)[2] ; a := 0 ; for p in f do a := a+wt(op(2, p)) ; end do: a ; end proc:
A177329 := proc(n) A064547(n!) ; end proc: seq(A177329(n), n=2..80) ; # R. J. Mathar, May 28 2010


MATHEMATICA

b[n_] := 2^(1 + Position[Reverse@IntegerDigits[n, 2], _?(# == 1 &)]) // Flatten; a[n_] := Module[{np = PrimePi[n]}, v = Table[0, {np}]; Do[p = Prime[k]; Do[v[[k]] += IntegerExponent[j, p], {j, 2, n}], {k, 1, np}]; Length[(b /@ v) // Flatten]]; Array[a, 77, 2] (* Amiram Eldar, Sep 17 2019*)


CROSSREFS

Cf. A050376, A176525, A001358, A176472, A176509, A064380, A050292.
Sequence in context: A065651 A322567 A221356 * A253852 A103672 A309255
Adjacent sequences: A177326 A177327 A177328 * A177330 A177331 A177332


KEYWORD

nonn


AUTHOR

Vladimir Shevelev, May 06 2010


EXTENSIONS

I inserted one omitted term: a(20)=10. Vladimir Shevelev, May 08 2010
Terms from a(14) onwards replaced according to the formula  R. J. Mathar, May 28 2010


STATUS

approved



