A305077 Partial sums of absolute values of A076191.

1, 1, 2, 3, 4, 5, 7, 8, 8, 9, 11, 13, 14, 14, 16, 19, 21, 23, 25, 26, 26, 27, 30, 32, 32, 33, 33, 35, 37, 39, 43, 46, 46, 46, 48, 51, 52, 52, 54, 57, 59, 61, 63, 63, 64, 65, 69, 72, 73, 74, 75, 77, 80, 82, 84, 86, 86, 87, 90, 93, 94, 95, 98, 102, 103, 105, 107, 108, 109, 111, 115, 119, 120, 121

Offset: 1

Author

Robert Israel, May 24 2018

Keywords

• nonn

Links

• Math Overflow, Asymptotic formula for absolute difference of number of prime factors between consecutive integers

Crossrefs

Cf. A001222, A076191.

Programs

Maple

L:= map(numtheory:-bigomega, [$1..200]):
ListTools:-PartialSums(map(abs, L[2..-1]-L[1..-2]));

Formula

a(n) = Sum_{k=1..n} |A001222(n+1) - A001222(n)|.