A159235 a(n) = smallest k having n prime factors such that k + sum of the prime factors of k also has n prime factors.

9, 63, 16, 162, 1904, 1056, 15984, 28000, 75520, 593280, 575424, 10209280, 58028032, 82616320, 755404800, 2255519744, 6636896256, 98721275904, 108417761280, 1303972577280, 2009909428224, 2344618524672, 50095111274496, 114342775226368, 456293923946496, 2380822275424256

Offset

2,1

Comments

The prime factors are counted with multiplicity, see A001222 and example.

Links

Table of n, a(n) for n=2..27.

Example

63 = 3*3*7 has three factors, and 63+3+3+7 = 76 = 2*2*19 also has three factors. 63 is smallest such number, hence a(3) = 63.

Prog

(Magma) cpf:=func< n | &+[a[2]: a in Factorization(n)] >; z:=20; S:=[ 0: n in [1..z] ]; for k in [2..1300000] do c:=cpf(k); if S[c] eq 0 and cpf(k + &+[ a[1]*a[2]: a in Factorization(k) ]) eq c then S[c]:=k; end if; end for; j:=2; while S[j] gt 0 do printf "%d, ", S[j]; j+:=1; end while;

Crossrefs

Cf. A001222 (number of prime divisors of n), A001414, A157973.

Sequence in context: A240391 A229701 A341627 * A181403 A292309 A337236

Adjacent sequences: A159232 A159233 A159234 * A159236 A159237 A159238

Keyword

nonn

Author

J. M. Bergot, Apr 06 2009

Extensions

Edited and a(6) - a(16) added by Klaus Brockhaus, Apr 08 2009

a(17) from Klaus Brockhaus, Apr 09 2009

Definition corrected by Donovan Johnson, May 09 2009

a(18)-a(24) from Donovan Johnson, May 08 2009

a(25)-a(27) from Daniel Suteu, Feb 05 2023

Status

approved