cp's OEIS Frontend

A348345 Number k such that k and k+1 have the same positive number of noninfinitary divisors (A348341).

%I A348345 #13 Oct 15 2021 05:55:34
%S A348345 44,75,98,116,147,171,242,243,244,332,387,507,548,603,604,724,735,819,
%T A348345 844,908,931,963,1035,1075,1083,1196,1251,1274,1275,1324,1412,1449,
%U A348345 1467,1556,1587,1665,1675,1772,1924,1925,1952,1988,2324,2331,2511,2523,2524,2540
%N A348345 Number k such that k and k+1 have the same positive number of noninfinitary divisors (A348341).
%C A348345 First differs from A049103 at n=17.
%C A348345 Numbers k such that A348341(k) = A348341(k+1) > 0.
%C A348345 The terms are restricted to have a positive number of noninfinitary divisors, since there are many consecutive numbers without noninfinitary divisors (these are the terms of A036537).
%H A348345 Amiram Eldar, <a href="/A348345/b348345.txt">Table of n, a(n) for n = 1..10000</a>
%e A348345 44 is a term since A348341(44) = A348341(45) = 2 > 0.
%t A348345 nid[1] = 0; nid[n_] := DivisorSigma[0, n] - Times @@ Flatten[2^DigitCount[#, 2, 1] & /@ FactorInteger[n][[;; , 2]]]; Select[Range[2500],(nid1 = nid[#]) > 0 && nid1 == nid[# + 1] &]
%o A348345 (PARI)
%o A348345 A348341(n) = (numdiv(n)-factorback(apply(a -> 2^hammingweight(a), factorint(n)[, 2])));
%o A348345 isA348345(n) = { my(u=A348341(n)); (u>0&&(A348341(1+n)==u)); }; \\ _Antti Karttunen_, Oct 13 2021
%Y A348345 Cf. A036537, A049103, A348341, A348346.
%Y A348345 Subsequence of A162643.
%Y A348345 Similar sequences: A005237, A006049, A343819, A344312, A344313, A344314.
%K A348345 nonn
%O A348345 1,1
%A A348345 _Amiram Eldar_, Oct 13 2021