A354363 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).

1, 4, 6, 13, 8, 12, 12, 40, 31, 8, 14, 78, 18, 12, 24, 121, 20, 124, 24, 104, 12, 28, 30, 120, 57, 36, 156, 156, 32, 24, 38, 364, 42, 20, 24, 403, 42, 24, 18, 40, 44, 12, 48, 182, 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

Offset: 1

Author

Antti Karttunen, May 30 2022

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..20000
• Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537
• Index entries for sequences computed from indices in prime factorization
• Index entries for sequences related to sigma(n)

Crossrefs

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

Programs

PARI

A003961(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
A353783(n) = { my(f=factor(n)~); lcm(vector(#f, i, sigma(f[1, i]^f[2, i]))); };
A354363(n) = A353783(A003961(n));

PARI

A003973(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); sigma(factorback(f)); };
A354363(n) = { my(f=factor(n)~); lcm(vector(#f, i, A003973(f[1, i]^f[2, i]))); };

Formula

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

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

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