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a(n) = LCM_{p^e||n} (q^(e+1)-1)/(q-1), when n = Product_{p^e||n}, with each p^e the maximal power of prime p that divides n, and q = nextPrime(p).
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%I #15 Jun 02 2022 14:48:20

%S 1,4,6,13,8,12,12,40,31,8,14,78,18,12,24,121,20,124,24,104,12,28,30,

%T 120,57,36,156,156,32,24,38,364,42,20,24,403,42,24,18,40,44,12,48,182,

%U 248,60,54,726,133,228,60,234,60,156,56,120,24,32,62,312,68,76,372,1093,72,84,72,260,30,24,74,1240,80,84

%N a(n) = LCM_{p^e||n} (q^(e+1)-1)/(q-1), when n = Product_{p^e||n}, with each p^e the maximal power of prime p that divides n, and q = nextPrime(p).

%H Antti Karttunen, <a href="/A354363/b354363.txt">Table of n, a(n) for n = 1..20000</a>

%H Antti Karttunen, <a href="/A354363/a354363.txt">Data supplement: n, a(n) computed for n = 1..65537</a>

%H <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>

%H <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>

%F a(n) = LCM_{p^e||n} A003973(p^e), when n = Product_{p^e||n}.

%F a(n) = A353783(A003961(n)).

%F a(n) = A003973(n) / A354364(n).

%o (PARI)

%o A003961(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };

%o A353783(n) = { my(f=factor(n)~); lcm(vector(#f, i, sigma(f[1, i]^f[2, i]))); };

%o A354363(n) = A353783(A003961(n));

%o (PARI)

%o A003973(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); sigma(factorback(f)); };

%o A354363(n) = { my(f=factor(n)~); lcm(vector(#f, i, A003973(f[1, i]^f[2, i]))); };

%Y Cf. A003961, A003973, A151800, A353783, A354364.

%K nonn

%O 1,2

%A _Antti Karttunen_, May 30 2022