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

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

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