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%I #20 May 15 2020 09:06:08
%S 1,2,8,7,7,10,8,9,15,97,26,75,16,356,39,96,39,39,39,264,470,776,97,
%T 711,249,765,4458,334,699,1084,18911,7150,1447,4604,1399,446,36041,
%U 5836,3504,1449,4359,6034,688,60818,4514,90825,34641,36852,77173,11100,2564
%N Least k > n such that p(n) divides p(k), where p(k) denotes the k-th partition number (A000041).
%C A000041(a(n)) mod A000041(n) = 0. - _Reinhard Zumkeller_, Aug 22 2003
%H Amiram Eldar, <a href="/A079031/b079031.txt">Table of n, a(n) for n = 0..72</a>
%e a(19)=264: A000041(264) = 670448123060170 = 2*5*(7^2)*13*41*1907*1346143 = (13*41*1907*1346143)*(2*5*7^2) = 1368261475633*490 = 1368261475633*A000041(19).
%t Do[m = PartitionsP[n]; k = n + 1; While[Mod[PartitionsP[k], m] > 0, k++ ]; Print[k], {n, 0, 50}] (* _Ryan Propper_, Oct 31 2005 *)
%o (PARI) a(n) = my(k=n+1, p=numbpart(n)); while (numbpart(k) % p, k++); k; \\ _Michel Marcus_, May 15 2020
%Y Cf. A000041.
%K nonn
%O 0,2
%A _Benoit Cloitre_, Feb 01 2003
%E More terms from _Reinhard Zumkeller_, Aug 22 2003
%E Further terms from _Ryan Propper_, Oct 31 2005
%E a(0) inserted by _Amiram Eldar_, May 15 2020
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