A183100 a(n) is the sum of divisors d of n which are either 1 or of the form Product_{i} (p_i^e_i) where at least one e_i = 1.
1, 3, 4, 3, 6, 12, 8, 3, 4, 18, 12, 24, 14, 24, 24, 3, 18, 30, 20, 38, 32, 36, 24, 48, 6, 42, 4, 52, 30, 72, 32, 3, 48, 54, 48, 42, 38, 60, 56, 78, 42, 96, 44, 80, 69, 72, 48, 96, 8, 68, 72, 94, 54, 84, 72, 108, 80, 90, 60, 164, 62, 96, 95, 3, 84, 144, 68, 122, 96, 144, 72, 66, 74, 114, 99, 136, 96, 168, 80, 158, 4, 126, 84, 220, 108, 132, 120, 168, 90, 225, 112, 164, 128, 144, 120, 192, 98, 122, 147, 88
Offset: 1
Examples
For n = 12, the set of such divisors is {1, 2, 3, 6, 12}; a(12) = 1+2+3+6+12 = 24.
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Programs
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Mathematica
f1[p_, e_] := (p^(e+1)-1)/(p-1); f2[p_, e_] := f1[p, e] - p; a[1] = 1; a[n_] := Times @@ f1 @@@ (f = FactorInteger[n]) - Times @@ f2 @@@ f + 1; Array[a, 100] (* Amiram Eldar, Aug 29 2023 *)
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PARI
A183100(n) = (1 + sumdiv(n, d, d*(!ispowerful(d)))); \\ Antti Karttunen, Oct 07 2017
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