%I #7 May 15 2022 11:47:54
%S 1,3,5,7,11,13,15,17,19,21,23,25,29,31,33,35,37,39,41,43,47,49,51,53,
%T 55,57,59,61,65,67,69,71,73,77,79,83,85,87,89,91,93,95,97,101,103,105,
%U 107,109,111,113,115,119,121,123,127,129,131,133,137,139,141
%N Numbers whose weakly increasing prime indices y have no fixed points y(i) = i.
%C First differs from A325128 in lacking 75.
%C 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.
%C All terms are odd.
%e The terms together with their prime indices begin:
%e 1: {} 35: {3,4} 69: {2,9} 105: {2,3,4}
%e 3: {2} 37: {12} 71: {20} 107: {28}
%e 5: {3} 39: {2,6} 73: {21} 109: {29}
%e 7: {4} 41: {13} 77: {4,5} 111: {2,12}
%e 11: {5} 43: {14} 79: {22} 113: {30}
%e 13: {6} 47: {15} 83: {23} 115: {3,9}
%e 15: {2,3} 49: {4,4} 85: {3,7} 119: {4,7}
%e 17: {7} 51: {2,7} 87: {2,10} 121: {5,5}
%e 19: {8} 53: {16} 89: {24} 123: {2,13}
%e 21: {2,4} 55: {3,5} 91: {4,6} 127: {31}
%e 23: {9} 57: {2,8} 93: {2,11} 129: {2,14}
%e 25: {3,3} 59: {17} 95: {3,8} 131: {32}
%e 29: {10} 61: {18} 97: {25} 133: {4,8}
%e 31: {11} 65: {3,6} 101: {26} 137: {33}
%e 33: {2,5} 67: {19} 103: {27} 139: {34}
%t pq[y_]:=Length[Select[Range[Length[y]],#==y[[#]]&]];
%t Select[Range[100],pq[Flatten[Cases[FactorInteger[#],{p_,k_}:>Table[PrimePi[p],{k}]]]]==0&]
%Y * = unproved
%Y These partitions are counted by A238394, strict A025147.
%Y These are the zeros of A352822.
%Y *The reverse version is A352826, counted by A064428 (strict A352828).
%Y *The complement reverse version is A352827, counted by A001522.
%Y The complement is A352872, counted by A238395.
%Y A000700 counts self-conjugate partitions, ranked by A088902.
%Y A001222 counts prime indices, distinct A001221.
%Y A008290 counts permutations by fixed points, nonfixed A098825.
%Y A056239 adds up prime indices, row sums of A112798 and A296150.
%Y A114088 counts partitions by excedances.
%Y A115720 and A115994 count partitions by their Durfee square.
%Y A122111 represents partition conjugation using Heinz numbers.
%Y A124010 gives prime signature, sorted A118914, conjugate rank A238745.
%Y A238349 counts compositions by fixed points, complement A352523.
%Y A238352 counts reversed partitions by fixed points.
%Y A352833 counts partitions by fixed points.
%Y Cf. A062457, A064410, A065770, A093641, A257990, A342192, A352486, A352823, A352824, A352825, A352831.
%K nonn
%O 1,2
%A _Gus Wiseman_, Apr 06 2022