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A337538
a(n) is the least k such that A003961(k*A071395(n)) is abundant.
2
6, 6, 15, 15, 15, 15, 15, 15, 3, 6, 6, 6, 9, 2, 15, 15, 15, 3, 15, 2, 15, 3, 15, 15, 6, 3, 2, 3, 3, 3, 9, 3, 9, 3, 3, 3, 2, 15, 6, 15, 6, 3, 2, 15, 15, 15, 3, 15, 15, 15, 3, 15, 15, 3, 15, 15, 2, 15, 15, 15, 15, 2, 3, 15, 2, 15, 15, 15, 2, 15, 15, 15, 15, 2, 15, 15, 15, 15, 15, 15, 2, 2, 15, 15, 15, 15, 2
OFFSET
1,1
COMMENTS
A071395(n) is the n-th primitive abundant number. A003961(k) replaces each prime factor of k with the next larger prime.
See also the table in the example section of A337469.
LINKS
FORMULA
a(n) = A337469(n) / A071395(n).
MATHEMATICA
Map[Block[{k = 1}, While[DivisorSigma[1, #] <= 2 # &[Times @@ Map[#1^#2 & @@ # &, FactorInteger[k #] /. {p_, e_} /; e > 0 :> {Prime[PrimePi@ p + 1], e}]], k++]; k] &, Select[Range[10^4], DivisorSigma[1, #] > 2 # && Times @@ Boole@ Map[DivisorSigma[1, #] < 2 # &, Most@ Divisors@ #] == 1 &]] (* Michael De Vlieger, Oct 05 2020 *)
PROG
(PARI)
isA071395(n) = if(sigma(n) <= 2*n, 0, fordiv(n, d, if((d != n)&&(sigma(d) >= 2*d), return(0))); (1)); \\ After code in A071395
A003961(n) = { my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
isA337386(n) = { my(x=A003961(n)); (sigma(x)>=2*x); };
for(n=1, 2^13, if(isA071395(n), i=0; for(k=1, oo, if(isA337386(k*n), i++; print1(k, ", "); break))));
KEYWORD
nonn
AUTHOR
Antti Karttunen and Peter Munn, Sep 07 2020
STATUS
approved