A392601 Numbers k such that A322582(k) <= A276085(k) <= A348507(k).

1, 2, 10, 15, 28, 42, 88, 132, 176, 198, 220, 416, 484, 624, 832, 936, 1040, 1053, 1092, 1144, 1170, 1248, 1300, 1404, 1456, 1560, 1638, 1664, 1716, 1755, 1820, 1872, 1950, 2028, 2080, 2106, 2176, 2184, 2288, 2340, 2457, 2548, 2574, 2704, 2730, 2860, 2925, 3042, 3146, 3264, 3380, 3808, 4056, 4080, 4352, 4459, 4563

Offset

1,2

Comments

A322582 and A348507 give lower and upper bounds for arithmetic derivative, A003415. See comments in A369650.

Among the initial 100000 terms, there are 9968 odd numbers, 8711 terms that are also in A048103, and only 34 squarefree terms (given in A392607).

Links

Antti Karttunen, Table of n, a(n) for n = 1..10000

Antti Karttunen, The first 100000 terms of sequence; all terms <= 5677350912

Prog

(PARI)
A003958(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1]--); factorback(f); };
A322582(n) = (n-A003958(n));
A003959(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1]++); factorback(f); };
A348507(n) = (A003959(n) - n);
is_A392601(n) = { my(f = factor(n), ul=A348507(n), pr=1, q=1, s=0); for(k=1, #f~, forprime(p = nextprime(1+q), f[k, 1]-1, pr *= p; if(pr > ul, return(0)); q = p); s += f[k, 2]*pr; if(s > ul, return(0))); (s >= A322582(n)); };

Crossrefs

Cf. A003415, A048103, A276085, A322582, A348507.

Subsequences: A369650, A392607 (squarefree terms).

Cf. also A392602.

Sequence in context: A212160 A134861 A063610 * A391864 A391865 A369650

Adjacent sequences: A392598 A392599 A392600 * A392602 A392603 A392604

Keyword

nonn

Author

Antti Karttunen, Jan 20 2026

Status

approved