A126272 a(1)=27; if n = Product p_i^e_i, n>1, then a(n) = Product p_{i+2}^{e_i+2}.

27, 125, 343, 625, 1331, 42875, 2197, 3125, 2401, 166375, 4913, 214375, 6859, 274625, 456533, 15625, 12167, 300125, 24389, 831875, 753571, 614125, 29791, 1071875, 14641, 857375, 16807, 1373125, 50653, 57066625, 68921, 78125, 1685159

Offset: 1

Author

Jonathan Vos Post, Mar 09 2007

Keywords

• easy
• nonn

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

Crossrefs

Cf. A000040, A045967, A065483, A353502.

Programs

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]

Formula

Sum_{n>=1} 1/a(n) = (72/95)*A065483 - 26/27. - Amiram Eldar, Aug 11 2022

Extensions

More terms from R. J. Mathar, Apr 20 2007