A348996 a(n) = usigma(A276086(n)), where usigma (A034448) is multiplicative with a(p^e) = (p^e)+1, and A276086 gives the prime product form of primorial base expansion of n.
1, 3, 4, 12, 10, 30, 6, 18, 24, 72, 60, 180, 26, 78, 104, 312, 260, 780, 126, 378, 504, 1512, 1260, 3780, 626, 1878, 2504, 7512, 6260, 18780, 8, 24, 32, 96, 80, 240, 48, 144, 192, 576, 480, 1440, 208, 624, 832, 2496, 2080, 6240, 1008, 3024, 4032, 12096, 10080, 30240, 5008, 15024, 20032, 60096, 50080, 150240, 50, 150
Offset: 0
Programs
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PARI
A348996(n) = { my(m=1, p=2); while(n, if(n%p, m *= (1+(p^(n%p)))); n = n\p; p = nextprime(1+p)); (m); };