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A344572
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a(n) = Sum_{d|n} Omega(d!).
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1
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0, 1, 2, 5, 5, 10, 8, 16, 15, 21, 16, 33, 20, 31, 31, 44, 29, 55, 33, 61, 48, 57, 41, 89, 52, 70, 67, 90, 56, 113, 60, 109, 85, 99, 84, 153, 76, 112, 102, 156, 85, 166, 89, 153, 139, 139, 98, 220, 113, 176, 141, 187, 114, 225, 141, 225, 161, 185, 129, 305, 134, 197, 200, 254
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OFFSET
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1,3
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LINKS
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EXAMPLE
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a(10) = Sum_{d|10} Omega(d!) = Omega(1!) + Omega(2!) + Omega(5!) + Omega(10!) = 0 + 1 + 5 + 15 = 21.
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MATHEMATICA
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Table[Sum[PrimeOmega[k!] (1 - Ceiling[n/k] + Floor[n/k]), {k, n}], {n, 100}]
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PROG
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(PARI) first(n) = { my(v = vector(n), res = vector(n), d); for(i = 2, n, v[i] = v[i-1] + bigomega(i); ); for(i = 2, n, d = divisors(i); res[i] = sum(i = 2, #d, v[d[i]]) ); res } \\ David A. Corneth, May 23 2021
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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