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

Author

Amiram Eldar, Oct 13 2021

Keywords

• nonn

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).

Examples

			44 is a term since A348341(44) = A348341(45) = 2 > 0.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A036537, A049103, A348341, A348346.

Subsequence of A162643.

Similar sequences: A005237, A006049, A343819, A344312, A344313, A344314.

Programs

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] &]

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