cp's OEIS Frontend

A352830 Numbers whose weakly increasing prime indices y have no fixed points y(i) = i.

%I A352830 #7 May 15 2022 11:47:54
%S A352830 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 A352830 55,57,59,61,65,67,69,71,73,77,79,83,85,87,89,91,93,95,97,101,103,105,
%U A352830 107,109,111,113,115,119,121,123,127,129,131,133,137,139,141
%N A352830 Numbers whose weakly increasing prime indices y have no fixed points y(i) = i.
%C A352830 First differs from A325128 in lacking 75.
%C A352830 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 A352830 All terms are odd.
%e A352830 The terms together with their prime indices begin:
%e A352830       1: {}        35: {3,4}     69: {2,9}     105: {2,3,4}
%e A352830       3: {2}       37: {12}      71: {20}      107: {28}
%e A352830       5: {3}       39: {2,6}     73: {21}      109: {29}
%e A352830       7: {4}       41: {13}      77: {4,5}     111: {2,12}
%e A352830      11: {5}       43: {14}      79: {22}      113: {30}
%e A352830      13: {6}       47: {15}      83: {23}      115: {3,9}
%e A352830      15: {2,3}     49: {4,4}     85: {3,7}     119: {4,7}
%e A352830      17: {7}       51: {2,7}     87: {2,10}    121: {5,5}
%e A352830      19: {8}       53: {16}      89: {24}      123: {2,13}
%e A352830      21: {2,4}     55: {3,5}     91: {4,6}     127: {31}
%e A352830      23: {9}       57: {2,8}     93: {2,11}    129: {2,14}
%e A352830      25: {3,3}     59: {17}      95: {3,8}     131: {32}
%e A352830      29: {10}      61: {18}      97: {25}      133: {4,8}
%e A352830      31: {11}      65: {3,6}    101: {26}      137: {33}
%e A352830      33: {2,5}     67: {19}     103: {27}      139: {34}
%t A352830 pq[y_]:=Length[Select[Range[Length[y]],#==y[[#]]&]];
%t A352830 Select[Range[100],pq[Flatten[Cases[FactorInteger[#],{p_,k_}:>Table[PrimePi[p],{k}]]]]==0&]
%Y A352830 * = unproved
%Y A352830 These partitions are counted by A238394, strict A025147.
%Y A352830 These are the zeros of A352822.
%Y A352830 *The reverse version is A352826, counted by A064428 (strict A352828).
%Y A352830 *The complement reverse version is A352827, counted by A001522.
%Y A352830 The complement is A352872, counted by A238395.
%Y A352830 A000700 counts self-conjugate partitions, ranked by A088902.
%Y A352830 A001222 counts prime indices, distinct A001221.
%Y A352830 A008290 counts permutations by fixed points, nonfixed A098825.
%Y A352830 A056239 adds up prime indices, row sums of A112798 and A296150.
%Y A352830 A114088 counts partitions by excedances.
%Y A352830 A115720 and A115994 count partitions by their Durfee square.
%Y A352830 A122111 represents partition conjugation using Heinz numbers.
%Y A352830 A124010 gives prime signature, sorted A118914, conjugate rank A238745.
%Y A352830 A238349 counts compositions by fixed points, complement A352523.
%Y A352830 A238352 counts reversed partitions by fixed points.
%Y A352830 A352833 counts partitions by fixed points.
%Y A352830 Cf. A062457, A064410, A065770, A093641, A257990, A342192, A352486, A352823, A352824, A352825, A352831.
%K A352830 nonn
%O A352830 1,2
%A A352830 _Gus Wiseman_, Apr 06 2022