A337538 a(n) is the least k such that A003961(k*A071395(n)) is abundant.

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

Antti Karttunen, Table of n, a(n) for n = 1..13037

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))));

Crossrefs

Cf. A000203, A003961, A003973, A071395, A337386, A337469, A337479.

Sequence in context: A330568 A085596 A107620 * A315809 A168414 A266223

Adjacent sequences: A337535 A337536 A337537 * A337539 A337540 A337541

Keyword

nonn

Author

Antti Karttunen and Peter Munn, Sep 07 2020

Status

approved