A083262 a(n) = sigma(A046523(n)), sum of divisors of the least number with the same prime signature as n.

1, 3, 3, 7, 3, 12, 3, 15, 7, 12, 3, 28, 3, 12, 12, 31, 3, 28, 3, 28, 12, 12, 3, 60, 7, 12, 15, 28, 3, 72, 3, 63, 12, 12, 12, 91, 3, 12, 12, 60, 3, 72, 3, 28, 28, 12, 3, 124, 7, 28, 12, 28, 3, 60, 12, 60, 12, 12, 3, 168, 3, 12, 28, 127, 12, 72, 3, 28, 12, 72, 3, 195, 3, 12, 28, 28, 12, 72

Offset: 1

Author

Labos Elemer, May 09 2003

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000203, A046523, A276528, A286360.

Programs

Mathematica

Table[DivisorSigma[1, Times @@ MapIndexed[Prime[First@ #2]^#1 &, Sort[FactorInteger[n][[All, -1]], Greater]] - Boole[n == 1]], {n, 78}] (* Michael De Vlieger, May 20 2017 *)

PARI

A046523(n) = my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]) \\ This function from Charles R Greathouse IV, Aug 17 2011
A083262(n) = sigma(A046523(n)); \\ Antti Karttunen, May 19 2017

Extensions

Name clarified by Antti Karttunen, May 19 2017