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A069915 Sum of (1+phi)-divisors of n (cf. A061389).

%I A069915 #19 Aug 15 2023 02:08:31
%S A069915 1,3,4,3,6,12,8,7,4,18,12,12,14,24,24,11,18,12,20,18,32,36,24,28,6,42,
%T A069915 13,24,30,72,32,31,48,54,48,12,38,60,56,42,42,96,44,36,24,72,48,44,8,
%U A069915 18,72,42,54,39,72,56,80,90,60,72,62,96,32,35,84,144,68,54,96,144,72
%N A069915 Sum of (1+phi)-divisors of n (cf. A061389).
%H A069915 Reinhard Zumkeller, <a href="/A069915/b069915.txt">Table of n, a(n) for n = 1..10000</a>
%F A069915 Multiplicative with a(p^e) = 1+Sum_{k=1..e, gcd(k, e)=1} p^k.
%t A069915 a[1] = 1; a[p_?PrimeQ] = p + 1; a[n_] := Times @@ (1 + Sum[If[GCD[k, Last[#]] == 1, First[#]^k, 0], {k, 1, Last[#]}] & ) /@ FactorInteger[n]; Table[a[n], {n, 1, 71}] (* _Jean-François Alcover_, May 04 2012 *)
%o A069915 (Haskell)
%o A069915 a069915 n = product $ zipWith sum_1phi (a027748_row n) (a124010_row n)
%o A069915    where sum_1phi p e = 1 + sum [p ^ k | k <- a038566_row e]
%o A069915 -- _Reinhard Zumkeller_, Mar 13 2012
%o A069915 (PARI) a(n) = {my(f = factor(n)); prod(i = 1, #f~, 1 + sum(k = 1, f[i, 2], (gcd(k, f[i, 2]) == 1) * f[i, 1]^k));} \\ _Amiram Eldar_, Aug 15 2023
%Y A069915 Cf. A061389.
%Y A069915 Cf. A027748, A124010, A038566, A051378.
%K A069915 mult,nonn
%O A069915 1,2
%A A069915 _Vladeta Jovovic_, Apr 23 2002