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a(n) = Sum_{k=1..n} 3^Omega(k).
4

%I #18 Sep 07 2023 12:50:04

%S 1,4,7,16,19,28,31,58,67,76,79,106,109,118,127,208,211,238,241,268,

%T 277,286,289,370,379,388,415,442,445,472,475,718,727,736,745,826,829,

%U 838,847,928,931,958,961,988,1015,1024,1027,1270,1279,1306,1315,1342,1345,1426,1435,1516,1525,1534,1537,1618

%N a(n) = Sum_{k=1..n} 3^Omega(k).

%D Tenenbaum, G. (2015). Introduction to analytic and probabilistic number theory, 3rd ed., American Mathematical Soc. See page 59.

%H Vaclav Kotesovec, <a href="/A350961/b350961.txt">Table of n, a(n) for n = 1..10000</a>

%t Accumulate[3^PrimeOmega[Range[100]]] (* _Vaclav Kotesovec_, Feb 16 2022 *)

%o (Python)

%o from sympy.ntheory.factor_ import primeomega

%o def A350961(n): return sum(3**primeomega(m) for m in range(1,n+1)) # _Chai Wah Wu_, Sep 07 2023

%Y Cf. A001222 (Omega), A069205, A069212. Partial sums of A165824.

%K nonn,easy

%O 1,2

%A _N. J. A. Sloane_, Feb 06 2022