cp's OEIS Frontend

A352823 Number of nonfixed points y(i) != i, where y is the weakly increasing sequence of prime indices of n.

%I A352823 #14 May 15 2022 11:46:40
%S A352823 0,0,1,1,1,0,1,2,1,1,1,2,1,1,2,3,1,1,1,1,2,1,1,3,2,1,2,2,1,0,1,4,2,1,
%T A352823 2,3,1,1,2,3,1,1,1,2,1,1,1,4,2,1,2,2,1,2,2,2,2,1,1,3,1,1,2,5,2,1,1,2,
%U A352823 2,2,1,4,1,1,2,2,2,1,1,4,3,1,1,2,2,1,2,3,1,2,2,2,2,1,2,5,1,2,2,2,1,1,1,3,3
%N A352823 Number of nonfixed points y(i) != i, where y is the weakly increasing sequence of prime indices of n.
%C A352823 A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798.
%H A352823 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%F A352823 a(n) = A001222(n) - A352822(n). - _Antti Karttunen_, Apr 11 2022
%e A352823 The prime indices of 6500 are {1,1,3,3,3,6}, with nonfixed points at positions {2,4,5}, so a(6500) = 3.
%t A352823 pnq[y_]:=Length[Select[Range[Length[y]],#!=y[[#]]&]];
%t A352823 Table[pnq[If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]]],{n,100}]
%o A352823 (PARI) A352823(n) = { my(f=factor(n),i=0,c=0); for(k=1,#f~,while(f[k,2], f[k,2]--; i++; c += (i!=primepi(f[k,1])))); (c); }; \\ _Antti Karttunen_, Apr 11 2022
%Y A352823 * = unproved
%Y A352823 Positions of zeros are A002110
%Y A352823 Positions of first appearances are A077552.
%Y A352823 The complement triangle version is A238352.
%Y A352823 A version for compositions is A352513, complement A352512.
%Y A352823 The complement is A352822.
%Y A352823 The reverse version is A352825, complement A352824.
%Y A352823 Complement positions of 1's are A352831, counted by A352832.
%Y A352823 A000700 counts self-conjugate partitions, ranked by A088902.
%Y A352823 A001222 counts prime indices, distinct A001221.
%Y A352823 *A001522 counts partitions with a fixed point, ranked by A352827.
%Y A352823 A056239 adds up prime indices, row sums of A112798 and A296150.
%Y A352823 *A064428 counts partitions without a fixed point, ranked by A352826.
%Y A352823 A122111 represents partition conjugation using Heinz numbers.
%Y A352823 A124010 gives prime signature, sorted A118914, conjugate rank A238745.
%Y A352823 A115720 and A115994 count partitions by their Durfee square.
%Y A352823 A238394 counts reversed partitions without a fixed point, ranked by A352830.
%Y A352823 A238395 counts reversed partitions with a fixed point, ranked by A352872.
%Y A352823 A352833 counts partitions by fixed points, rank statistic A352824.
%Y A352823 Cf. A065770, A093641, A114088, A252464, A257990, A325163, A325164, A325165, A325169, A342192, A352486-A352491, A352828, A352829.
%K A352823 nonn
%O A352823 1,8
%A A352823 _Gus Wiseman_, Apr 05 2022
%E A352823 Data section extended up to 105 terms by _Antti Karttunen_, Apr 11 2022