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A345315 a(n) = Sum_{d|n} d^[Omega(d) = 2], where [ ] is the Iverson bracket. 0
1, 2, 2, 6, 2, 9, 2, 7, 11, 13, 2, 14, 2, 17, 18, 8, 2, 19, 2, 18, 24, 25, 2, 16, 27, 29, 12, 22, 2, 36, 2, 9, 36, 37, 38, 25, 2, 41, 42, 20, 2, 46, 2, 30, 28, 49, 2, 18, 51, 39, 54, 34, 2, 21, 58, 24, 60, 61, 2, 43, 2, 65, 34, 10, 68, 66, 2, 42, 72, 64, 2, 28, 2, 77, 44, 46, 80 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
For each divisor d of n, add d if d is semiprime, otherwise add 1. For example, the divisors of 24 are: 1, 2, 3, 4, 6, 8, 12, 24, and the only semiprime divisors of 24 are 4 and 6, so a(24) = 1 + 1 + 1 + 4 + 6 + 1 + 1 + 1 = 16.
LINKS
FORMULA
a(p) = Sum_{d|p} d^[Omega(d) = 2] = 1^0 + p^0 = 2, for primes p.
EXAMPLE
a(n) = Sum_{d|12} d^[Omega(d) = 2] = 1^0 + 2^0 + 3^0 + 4^1 + 6^1 + 12^0 = 14.
MATHEMATICA
Table[Sum[k^KroneckerDelta[PrimeOmega[k], 2] (1 - Ceiling[n/k] + Floor[n/k]), {k, n}], {n, 100}]
PROG
(PARI) a(n) = sumdiv(n, d, if (bigomega(d)==2, d, 1)); \\ Michel Marcus, Jun 13 2021
CROSSREFS
Cf. A001222 (Omega).
Sequence in context: A291840 A208448 A096869 * A154009 A297792 A266722
KEYWORD
nonn
AUTHOR
Wesley Ivan Hurt, Jun 13 2021
STATUS
approved

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Last modified July 14 02:38 EDT 2024. Contains 374291 sequences. (Running on oeis4.)