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A344572 a(n) = Sum_{d|n} Omega(d!). 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

David A. Corneth, Table of n, a(n) for n = 1..10000

EXAMPLE

a(10) = Sum_{d|10} Omega(d!) = Omega(1!) + Omega(2!) + Omega(5!) + Omega(10!) = 0 + 1 + 5 + 15 = 21.

MATHEMATICA

Table[Sum[PrimeOmega[k!] (1 - Ceiling[n/k] + Floor[n/k]), {k, n}], {n, 100}]

PROG

(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

CROSSREFS

Cf. A000142, A001222 (Omega), A022559.

Sequence in context: A059797 A173567 A288726 * A265129 A212624 A351475

Adjacent sequences:  A344569 A344570 A344571 * A344573 A344574 A344575

KEYWORD

nonn

AUTHOR

Wesley Ivan Hurt, May 23 2021

STATUS

approved

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Last modified May 24 07:35 EDT 2022. Contains 354005 sequences. (Running on oeis4.)