OFFSET
1,1
COMMENTS
Analog of A045967 a(1)=4; if n = Product p_i^e_i, n>1, then a(n) = Product p_{i+1}^{e_i+1}. In a sense, n is the zeroth sequence in a family of sequences, A045967 is the first sequence in a family of sequences and a(n) is the second sequence in a family of sequences.
If we had a(1) = 1 (instead of 4), then this would be multiplicative and a permutation of A353502. - Amiram Eldar, Aug 11 2022
FORMULA
Sum_{n>=1} 1/a(n) = (72/95)*A065483 - 26/27. - Amiram Eldar, Aug 11 2022
MAPLE
A126272 := proc(n) local pf, i, p, e, resul ; if n = 1 then 27 ; else pf := ifactors(n)[2] ; resul := 1 ; for i from 1 to nops(pf) do p := op(1, op(i, pf)) ; e := op(2, op(i, pf)) ; resul := resul * nextprime(nextprime(p))^(e+2) ; od ; resul ; fi ; end: for n from 1 to 40 do printf("%d, ", A126272(n)) ; od ; # R. J. Mathar, Apr 20 2007
MATHEMATICA
f[p_, e_] := NextPrime[p, 2]^(e + 2); a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100]
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Jonathan Vos Post, Mar 09 2007
EXTENSIONS
More terms from R. J. Mathar, Apr 20 2007
STATUS
approved