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 A348345 Number k such that k and k+1 have the same positive number of noninfinitary divisors (A348341). 4
 44, 75, 98, 116, 147, 171, 242, 243, 244, 332, 387, 507, 548, 603, 604, 724, 735, 819, 844, 908, 931, 963, 1035, 1075, 1083, 1196, 1251, 1274, 1275, 1324, 1412, 1449, 1467, 1556, 1587, 1665, 1675, 1772, 1924, 1925, 1952, 1988, 2324, 2331, 2511, 2523, 2524, 2540 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS First differs from A049103 at n=17. Numbers k such that A348341(k) = A348341(k+1) > 0. 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). LINKS Amiram Eldar, Table of n, a(n) for n = 1..10000 EXAMPLE 44 is a term since A348341(44) = A348341(45) = 2 > 0. MATHEMATICA 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] &] PROG (PARI) A348341(n) = (numdiv(n)-factorback(apply(a -> 2^hammingweight(a), factorint(n)[, 2]))); isA348345(n) = { my(u=A348341(n)); (u>0&&(A348341(1+n)==u)); }; \\ Antti Karttunen, Oct 13 2021 CROSSREFS Cf. A036537, A049103, A348341, A348346. Subsequence of A162643. Similar sequences: A005237, A006049, A343819, A344312, A344313, A344314. Sequence in context: A171665 A348098 A348076 * A049103 A074172 A039386 Adjacent sequences: A348342 A348343 A348344 * A348346 A348347 A348348 KEYWORD nonn AUTHOR Amiram Eldar, Oct 13 2021 STATUS approved

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Last modified February 23 11:40 EST 2024. Contains 370283 sequences. (Running on oeis4.)