OFFSET
1,2
COMMENTS
Multiplicative: If e = sum d_k 3^k, then a(p^e) = prod (d_k+1). - Christian G. Bower, May 19 2005
LINKS
Antti Karttunen, Table of n, a(n) for n = 1..10000
Frédéric Chyzak, Ivan Gutman, and Peter Paule, Predicting the number of hexagonal systems with 24 and 25 hexagons, Communications in Mathematical and Computer Chemistry (1999) No. 40, 139-151. See p. 141.
J. O. M. Pedersen, Tables of Aliquot Cycles [Broken link]
J. O. M. Pedersen, Tables of Aliquot Cycles [Via Internet Archive Wayback-Machine]
J. O. M. Pedersen, Tables of Aliquot Cycles [Cached copy, pdf file only]
FORMULA
a(1) = 1; for n > 1, a(n) = A006047(A067029(n)) * a(A028234(n)). [After Christian G. Bower's 2005 comment.] - Antti Karttunen, May 28 2017
EXAMPLE
2^3*3 is a 3-infinitary-divisor of 2^5*3^2 because 2^3*3 = 2^10*3^1 and 2^5*3^2 = 2^12*3^2 in ternary expanded power. All corresponding digits satisfy the condition. 1 <= 1, 0 <= 2, 1 <= 2.
MAPLE
A038148 := proc(n) if n= 1 then 1; else ifa := ifactors(n)[2] ;
a := 1; for f in ifa do e := convert(op(2, f), base, 3) ; a := a*mul(d+1, d=e) ; end do: end if; end proc:
seq(A038148(n), n=1..50) ; # R. J. Mathar, Feb 08 2011
MATHEMATICA
a[1] = 1; a[n_] := (k = 1; Do[k = k * Times @@ (IntegerDigits[f, 3] + 1), {f, FactorInteger[n][[All, 2]]}]; k); Table[a[n], {n, 1, 102}](* Jean-François Alcover, Feb 03 2012, after R. J. Mathar *)
PROG
(PARI)
A006047(n) = { my(m=1, d); while(n, d = (n%3); m *= (1+d); n = (n-d)/3); m; };
A038148(n) = factorback(apply(e -> A006047(e), factorint(n)[, 2])); \\ (After A037445) - Antti Karttunen, May 28 2017
CROSSREFS
KEYWORD
nonn,nice,easy,mult
AUTHOR
EXTENSIONS
More terms from Naohiro Nomoto, Jun 21 2001
Data section further extended to 105 terms by Antti Karttunen, May 28 2017
STATUS
approved