The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A284229 a(n) is the least k such that A073802(k) = n. 0
 1, 10, 12, 6, 336, 24, 5952, 168, 792, 496, 666624, 270, 10924032, 6720, 7344, 120, 3757637632, 4284, 45091651584, 2160, 79488, 1820672, 11544784011264, 672, 298080, 29331456, 106200, 13440, 53620880789471232, 10080, 1501384662105194496, 6552, 7022592, 7515275264 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Composite numbers that have just 1 as divisor that satisfies the condition for which sigma(k) / d_i is an integer are the Duffinian numbers (A003624). Alternative definition: Least k such that d(gcd(k,sigma(k)) = n. - Giovanni Resta, Mar 23 2017 LINKS EXAMPLE The divisors of 12 are 1, 2, 3, 4, 6, 12 and sigma(12) = 28. Then: 1) 28 / 1 = 28; 2) 28 / 2 = 14; 3) 28 / 4 = 7; and 12 is the least number to have this property. Therefore a(3) = 12. MAPLE with(numtheory): P:=proc(q) local k, n; for k from 1 to q do for n from 1 to q do if tau(gcd(n, sigma(n)))=k then print(n); break; fi; od; od; end: P(10^9); MATHEMATICA TakeWhile[#, # > 0 &] &@ Table[If[KeyExistsQ[#, n], First@ Lookup[#, n], -1], {n, Max@ Keys@ #}] &@ KeySort@ PositionIndex@ Table[DivisorSum[k, 1 &, IntegerQ[DivisorSigma[1, k]/#] &], {k, 10^6}] (* per Name, Version 10, or *) TakeWhile[#, # > 0 &] &@ Table[If[KeyExistsQ[#, n], First@ Lookup[#, n], -1], {n, Max@ Keys@ #}] &@ KeySort@ PositionIndex@ Table[DivisorSigma[0, GCD[k, DivisorSigma[1, k]]], {k, 10^7}] (* faster, Version 10, Michael De Vlieger, Mar 24 2017 *) PROG (PARI) nb(n) = my(s = sigma(n)); sumdiv(n, d, (s % d) == 0); a(n) = k=1; while(nb(k) != n, k++); k; \\ Michel Marcus, Mar 24 2017 CROSSREFS Cf. A000203, A003624, A073802. Sequence in context: A350444 A342356 A338290 * A078285 A303151 A103618 Adjacent sequences:  A284226 A284227 A284228 * A284230 A284231 A284232 KEYWORD nonn AUTHOR Paolo P. Lava, Mar 23 2017 EXTENSIONS a(13), a(17), a(19) and from a(22) to a(34) from Giovanni Resta, Mar 23 2017 Name proposed by Michel Marcus, Mar 24 2017 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified July 2 10:39 EDT 2022. Contains 355004 sequences. (Running on oeis4.)