cp's OEIS Frontend

A352872 Numbers whose weakly increasing prime indices y have a fixed point y(i) = i.

%I A352872 #8 May 15 2022 11:49:49
%S A352872 2,4,6,8,9,10,12,14,16,18,20,22,24,26,27,28,30,32,34,36,38,40,42,44,
%T A352872 45,46,48,50,52,54,56,58,60,62,63,64,66,68,70,72,74,75,76,78,80,81,82,
%U A352872 84,86,88,90,92,94,96,98,99,100,102,104,106,108,110,112,114
%N A352872 Numbers whose weakly increasing prime indices y have a fixed point y(i) = i.
%C A352872 First differs from A118672 in having 75.
%C A352872 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.
%e A352872 The terms together with their prime indices begin:
%e A352872       2: {1}           28: {1,1,4}         56: {1,1,1,4}
%e A352872       4: {1,1}         30: {1,2,3}         58: {1,10}
%e A352872       6: {1,2}         32: {1,1,1,1,1}     60: {1,1,2,3}
%e A352872       8: {1,1,1}       34: {1,7}           62: {1,11}
%e A352872       9: {2,2}         36: {1,1,2,2}       63: {2,2,4}
%e A352872      10: {1,3}         38: {1,8}           64: {1,1,1,1,1,1}
%e A352872      12: {1,1,2}       40: {1,1,1,3}       66: {1,2,5}
%e A352872      14: {1,4}         42: {1,2,4}         68: {1,1,7}
%e A352872      16: {1,1,1,1}     44: {1,1,5}         70: {1,3,4}
%e A352872      18: {1,2,2}       45: {2,2,3}         72: {1,1,1,2,2}
%e A352872      20: {1,1,3}       46: {1,9}           74: {1,12}
%e A352872      22: {1,5}         48: {1,1,1,1,2}     75: {2,3,3}
%e A352872      24: {1,1,1,2}     50: {1,3,3}         76: {1,1,8}
%e A352872      26: {1,6}         52: {1,1,6}         78: {1,2,6}
%e A352872      27: {2,2,2}       54: {1,2,2,2}       80: {1,1,1,1,3}
%e A352872 For example, the multiset {2,3,3} with Heinz number 75 has a fixed point at position 3, so 75 is in the sequence.
%t A352872 pq[y_]:=Length[Select[Range[Length[y]],#==y[[#]]&]];
%t A352872 Select[Range[100],pq[Flatten[Cases[FactorInteger[#],{p_,k_}:>Table[PrimePi[p],{k}]]]]>0&]
%Y A352872 * = unproved
%Y A352872 These partitions are counted by A238395, strict A096765.
%Y A352872 These are the nonzero positions in A352822.
%Y A352872 *The complement reverse version is A352826, counted by A064428.
%Y A352872 *The reverse version is A352827, counted by A001522 (strict A352829).
%Y A352872 The complement is A352830, counted by A238394 (strict A025147).
%Y A352872 A000700 counts self-conjugate partitions, ranked by A088902.
%Y A352872 A001222 counts prime indices, distinct A001221.
%Y A352872 A008290 counts permutations by fixed points, nonfixed A098825.
%Y A352872 A056239 adds up prime indices, row sums of A112798 and A296150.
%Y A352872 A114088 counts partitions by excedances.
%Y A352872 A115720 and A115994 count partitions by their Durfee square.
%Y A352872 A122111 represents partition conjugation using Heinz numbers.
%Y A352872 A124010 gives prime signature, sorted A118914, conjugate rank A238745.
%Y A352872 A238349 counts compositions by fixed points, complement A352523.
%Y A352872 A238352 counts reversed partitions by fixed points.
%Y A352872 A352833 counts partitions by fixed points.
%Y A352872 Cf. A062457, A064410, A065770, A093641, A257990, A325187, A342192, A352486, A352823, A352824, A352825, A352831, A352832.
%K A352872 nonn
%O A352872 1,1
%A A352872 _Gus Wiseman_, Apr 06 2022