A141565 Add 1 to all bases and exponents which are greater than 1 in the prime number decomposition of n.

2, 3, 4, 27, 6, 12, 8, 81, 64, 18, 12, 108, 14, 24, 24, 243, 18, 192, 20, 162, 32, 36, 24, 324, 216, 42, 256, 216, 30, 72, 32, 729, 48, 54, 48, 1728, 38, 60, 56, 486, 42, 96, 44, 324, 384, 72, 48, 972, 512, 648, 72, 378, 54, 768, 72, 648, 80, 90, 60, 648, 62, 96, 512

Offset

1,1

Comments

Start from the prime number decomposition of n, that is the list 1, 2, 3, 2^2, 5, 2*3, 7, 2^3, 3^2, 2*5, 11, 2^2*3... Add 1 to all visible bases and exponents (visible in the sense that exponents are not written down if they equal 1), that is 1+1, 2+1, 3+1, (2+1)^(2+1), 5+1, (2+1)*(3+1), 7+1, (2+1)^(3+1), (3+1)^(2+1), (2+1)*(5+1), 11+1, (2+1)^(2+1)*(3+1)..). Evaluate this modified product to yield a(n).

Links

Antti Karttunen, Table of n, a(n) for n = 1..16384

Maple

A := proc(n) local a, p, e, q, ifs ; ifs := ifactors(n)[2] ; if n = 1 then RETURN(2) fi; a := 1; for p in ifs do q := op(1, p)+1 ; if op(2, p) > 1 then e := op(2, p)+1 ; else e := 1 ; fi; a := a*q^e ; od: RETURN(a) ; end: for n from 1 to 120 do printf("%d, ", A(n)) ; od: # R. J. Mathar, Aug 21 2008

Mathematica

Array[Times @@ Apply[Times, FactorInteger[#] /. {{p_, e_} /; e > 1 :> (p + 1)^(e + 1), {k_, 1} :> k + 1}] &, 63] (* Michael De Vlieger, Nov 23 2017 *)

Prog

(PARI) A141565(n) = { if(1==n, return(2)); my(f=factor(n)); for(i=1, omega(n), f[i, 1] += 1; if(f[i, 2]>1, f[i, 2] += 1)); factorback(f); }; \\ Antti Karttunen, Nov 23 2017

Crossrefs

Cf. A000040, A002808.

Sequence in context: A044906 A255312 A293000 * A098549 A274677 A100604

Adjacent sequences: A141562 A141563 A141564 * A141566 A141567 A141568

Keyword

nonn

Author

Juri-Stepan Gerasimov, Aug 14 2008

Extensions

Edited and corrected by R. J. Mathar, Aug 21 2008

Status

approved