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%I #15 Dec 08 2022 12:38:41
%S 1,6,5,36,7,30,11,216,25,42,13,180,17,66,35,1296,19,150,23,252,55,78,
%T 29,1080,49,102,125,396,31,210,37,7776,65,114,77,900,41,138,85,1512,
%U 43,330,47,468,175,174,53,6480,121,294,95,612,59,750,91,2376,115,186,61,1260,67,222,275,46656,119,390,71,684,145,462,73,5400,79,246,245
%N a(n) = A003961(n)*A006519(n).
%C Completely multiplicative since both A003961 and A006519 are. - _Andrew Howroyd_, Jul 25 2018
%H Antti Karttunen, <a href="/A283980/b283980.txt">Table of n, a(n) for n = 1..10001</a>
%F a(n) = A003961(n)*A006519(n).
%F From _Michael De Vlieger_, Dec 29 2019: (Start)
%F a(p_k) = p_(k+1) for odd prime p.
%F a(2^k) = 6^k.
%F a(p_k#) = p_(k+1)# for p_k# = A002110(k). (End)
%e From _Michael De Vlieger_, Dec 29 2019: (Start)
%e a(1) = 1 since 1 is the empty product.
%e a(2) = 6 because 2 = 2^1 in form p_k^e; switching p_(k+1) for p, we have 3^1 = 3, and the largest power of 2 dividing 2 is 2^1 = 2; thus 3 * 2 = 6.
%e a(4) = 36 since 4 = 2^2 -> 4(3^2).
%e a(6) = 30 since 6 = 2^1 * 3^1 -> 2(3 * 5).
%e a(12) = 180 since 12 = 2^2 * 3 -> 4(3^2 * 5) = 4(45) = 180.
%e a(30) = 210 since 30 = 2 * 3 * 5 -> 2(3 * 5 * 7) = 210.
%e (End)
%t Array[(Times @@ Map[#1^#2 & @@ # &, FactorInteger[#] /. {p_, e_} /; e > 0 :> {Prime[PrimePi@ p + 1], e}] - Boole[# == 1])*2^IntegerExponent[#, 2] &, 75] (* _Michael De Vlieger_, Dec 29 2019 *)
%o (Scheme) (define (A283980 n) (* (A006519 n) (A003961 n)))
%o (PARI) a(n)={my(f=factor(n)); prod(i=1, #f~, my(p=f[i,1], e=f[i,2]); if(p==2, 6, nextprime(p+1))^e)} \\ _Andrew Howroyd_, Jul 25 2018
%o (Python)
%o from sympy import nextprime, factorint
%o from math import prod
%o def A283980(n): return prod(nextprime(p)**e if p > 2 else 6**e for p, e in factorint(n).items()) # _Chai Wah Wu_, Dec 08 2022
%Y Cf. A003961, A006519, A283477.
%K nonn,mult
%O 1,2
%A _Antti Karttunen_, Mar 19 2017
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