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 A177436 The number of positive integers m for which the exponents of 2 and p_n in the prime power factorization of m! are both powers of 2. 7
 7, 7, 6, 3, 4, 4, 3, 4, 8, 10, 2, 2, 2, 4, 6, 8, 10, 3, 2, 2, 2, 2, 4, 4, 4, 5, 6, 6, 6, 14, 3, 2, 2, 2, 2, 2, 2, 2, 4, 4, 4, 4, 4, 4, 4, 6, 6, 6, 8, 8, 8, 8, 12, 4, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 6, 6, 6, 6, 6, 6, 6 (list; graph; refs; listen; history; text; internal format)
 OFFSET 2,1 COMMENTS Or a(n) is the maximal m for which the Fermi-Dirac representation of m! (see comment in A050376) contains single power of 2 and single power of prime(n). LINKS Robert Price, Table of n, a(n) for n = 2..127 V. Shevelev, Compact integers and factorials, Acta Arithmetica 126 (2007), no. 3, 195-236. FORMULA a(2)=a(3)=7; a(4)=6; if p_n has the form (2^(4*k+1)+3)/5,k>=2,then a(n)=5; if p_n is a Fermat prime: p_n=2^(2^(k-1))+1, k>=3, then a(n)=4; if p_n has the form 2^k+3, k>=3, then a(n)=3; otherwise, if 2^(k-1)+3

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Last modified September 24 22:46 EDT 2021. Contains 347651 sequences. (Running on oeis4.)