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A241139 Number of nonprimes in factorization of n! over distinct terms of A050376. 4
0, 0, 1, 1, 2, 2, 3, 3, 3, 3, 4, 4, 5, 6, 7, 7, 4, 4, 5, 5, 6, 6, 8, 9, 10, 10, 9, 9, 11, 11, 12, 12, 10, 9, 8, 8, 9, 10, 11, 11, 12, 12, 11, 12, 14, 14, 16, 15, 15, 15, 13, 13, 14, 14, 14, 14, 16, 16, 16, 16, 17, 19, 21, 21, 18, 18, 19, 16, 14, 14, 16, 16, 17 (list; graph; refs; listen; history; text; internal format)
OFFSET
2,5
REFERENCES
V. S. Shevelev, Multiplicative functions in the Fermi-Dirac arithmetic, Izvestia Vuzov of the North-Caucasus region, Nature sciences 4 (1996), 28-43 [Russian].
LINKS
S. Litsyn and V. S. Shevelev, On factorization of integers with restrictions on the exponent, INTEGERS: Electronic Journal of Combinatorial Number Theory, 7 (2007), #A33, 1-36.
FORMULA
a(n) = A177329(n) - A055460(n).
EXAMPLE
Factorization of 4! over distinct terms of A050376 is 4! = 2*3*4. This factorization contains only one A050376-nonprime. So a(4)=1.
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[Select[(b /@ v) // Flatten, # > 1 &]]]; Array[a, 73, 2] (* Amiram Eldar, Sep 17 2019 *)
PROG
(PARI) a(n)={my(f=factor(n!)[, 2]); sum(i=1, #f~, hammingweight(f[i]>>1))} \\ Andrew Howroyd, Sep 17 2019
CROSSREFS
Sequence in context: A342678 A108356 A239499 * A294242 A241092 A055656
KEYWORD
nonn
AUTHOR
Vladimir Shevelev, Apr 16 2014
EXTENSIONS
More terms from Peter J. C. Moses, Apr 17 2014
STATUS
approved

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Last modified April 15 02:01 EDT 2024. Contains 371667 sequences. (Running on oeis4.)