A133904 - OEIS

A133904

a(n) = gcd(a(n-1),n-1)*a(n-1) + d(n-1) if a(n-1) is not divisible by 2, otherwise a(n) = a(n-1)/2, where gcd denotes common divisor, d(n) is number of divisors of n.

1, 2, 1, 3, 6, 3, 13, 15, 19, 22, 11, 123, 375, 377, 381, 1147, 1152, 576, 288, 144, 72, 36, 18, 9, 35, 178, 89, 93, 99, 101, 109, 111, 117, 355, 359, 363, 1098, 549, 553, 557, 565, 567, 11915, 11917, 11923, 11929, 11933, 11935, 11945, 11948, 5974, 2987, 2993

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

LINKS

Michael De Vlieger, Table of n, a(n) for n = 1..7154

MATHEMATICA

Nest[Append[#1, If[EvenQ@ Last[#1], Last[#1]/2, GCD[Last[#1], #2]*Last[#1] + DivisorSigma[0, #2]]] & @@ {#, Length[#]} &, {1}, 52] (* Michael De Vlieger, Mar 20 2022 *)

PROG

(PARI) lista(nn) = my(va = vector(nn)); va[1] = 1; for (n=2, nn, va[n] = if (va[n-1]%2, gcd(va[n-1], n-1)*va[n-1] + numdiv(n-1), va[n-1]/2); ); va; \\ Michel Marcus, Mar 21 2022

CROSSREFS

Cf. A001222, A000005.

Sequence in context: A193897 A226122 A347297 * A245182 A209160 A371418

Adjacent sequences: A133901 A133902 A133903 * A133905 A133906 A133907

KEYWORD

nonn

AUTHOR

Ctibor O. Zizka, Jan 07 2008

EXTENSIONS

Name and terms a(25) and following corrected by Jon E. Schoenfield, Mar 20 2022

STATUS

approved