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A361467
a(n) = A003961(n) * sigma(A003961(n)), where A003961 is fully multiplicative with a(p) = nextprime(p), and sigma is the sum of divisors function.
2
1, 12, 30, 117, 56, 360, 132, 1080, 775, 672, 182, 3510, 306, 1584, 1680, 9801, 380, 9300, 552, 6552, 3960, 2184, 870, 32400, 2793, 3672, 19500, 15444, 992, 20160, 1406, 88452, 5460, 4560, 7392, 90675, 1722, 6624, 9180, 60480, 1892, 47520, 2256, 21294, 43400, 10440, 2862, 294030, 16093, 33516, 11400
OFFSET
1,2
FORMULA
Multiplicative with a(p^e) = q^e * (q^(e+1) - 1) / (q - 1), where q = nextPrime(p).
a(n) = A003961(n) * A003973(n).
a(n) = A064987(A003961(n)).
MATHEMATICA
f[p_, e_] := (q = NextPrime[p])^e * (q^(e+1) - 1) / (q - 1); a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, May 18 2023 *)
PROG
(PARI)
A003961(n) = { my(f=factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); }; \\ From A003961
A361467(n) = { my(u=A003961(n)); (u*sigma(u)); };
CROSSREFS
KEYWORD
nonn,mult
AUTHOR
Antti Karttunen, Mar 20 2023
STATUS
approved