This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A340386 #8 Jan 25 2021 19:04:13 %S A340386 2,5,8,11,17,20,23,30,31,32,41,44,45,47,50,59,66,67,68,73,75,80,83,92, %T A340386 97,99,102,103,109,110,120,124,125,127,128,137,138,149,153,154,157, %U A340386 164,165,167,170,176,179,180,186,188,191,197,200,207,211,227,230 %N A340386 Heinz numbers of integer partitions with an odd number of parts, the greatest of which is odd. %C A340386 The Heinz number of a partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k). This gives a bijective correspondence between positive integers and integer partitions. %F A340386 Intersection of A026424 (odd length) and A244991 (odd maximum). %e A340386 The sequence of partitions together with their Heinz numbers begins: %e A340386 2: (1) 59: (17) 120: (3,2,1,1,1) %e A340386 5: (3) 66: (5,2,1) 124: (11,1,1) %e A340386 8: (1,1,1) 67: (19) 125: (3,3,3) %e A340386 11: (5) 68: (7,1,1) 127: (31) %e A340386 17: (7) 73: (21) 128: (1,1,1,1,1,1,1) %e A340386 20: (3,1,1) 75: (3,3,2) 137: (33) %e A340386 23: (9) 80: (3,1,1,1,1) 138: (9,2,1) %e A340386 30: (3,2,1) 83: (23) 149: (35) %e A340386 31: (11) 92: (9,1,1) 153: (7,2,2) %e A340386 32: (1,1,1,1,1) 97: (25) 154: (5,4,1) %e A340386 41: (13) 99: (5,2,2) 157: (37) %e A340386 44: (5,1,1) 102: (7,2,1) 164: (13,1,1) %e A340386 45: (3,2,2) 103: (27) 165: (5,3,2) %e A340386 47: (15) 109: (29) 167: (39) %e A340386 50: (3,3,1) 110: (5,3,1) 170: (7,3,1) %t A340386 Select[Range[100],OddQ[PrimeOmega[#]*PrimePi[FactorInteger[#][[-1,1]]]]&] %Y A340386 Note: Heinz numbers are given in parentheses below. %Y A340386 The case of odd length only is A026424. %Y A340386 The case of odd maximum only is A244991. %Y A340386 Positions of odd terms in A326846. %Y A340386 These partitions are counted by A340385. %Y A340386 The version for factorizations is A340607. %Y A340386 A000009 counts partitions into odd parts (A066208). %Y A340386 A027193 counts partitions of odd length, or of odd maximum. %Y A340386 A061395 gives maximum prime index. %Y A340386 A106529 lists numbers with Omega equal to maximum prime index. %Y A340386 A160786 counts odd-length partitions of odd numbers (A300272). %Y A340386 A339890 counts factorizations of odd length. %Y A340386 A340102 counts odd-length factorizations into odd factors. %Y A340386 Cf. A001222, A027187, A056239, A112798, A236914, A258116, A300063, A324522, A340608, A340788, A340831. %K A340386 nonn %O A340386 1,1 %A A340386 _Gus Wiseman_, Jan 25 2021