A280286 a(n) is the least k such that sopfr(k) - sopf(k) = n.

4, 9, 8, 25, 16, 49, 32, 81, 64, 121, 128, 169, 256, 625, 512, 289, 1024, 361, 2048, 1444, 1331, 529, 5324, 2116, 2197, 4232, 8788, 841, 17576, 961, 7569, 3844, 4913, 7688, 19652, 1369, 6859, 5476, 12321, 1681, 34225, 1849, 15129, 7396, 12167, 2209, 46225, 8836, 19881

Offset

2,1

Links

Michel Marcus, Table of n, a(n) for n = 2..500

Formula

For p prime, a(p) = p^2 (see A001248).

Mathematica

prifacs[n_]:=If[n==1, {}, Flatten[Apply[ConstantArray, FactorInteger[n], {1}]]];
q=Table[Total[prifacs[n]]-Total[Union[prifacs[n]]], {n, 1000}];
mnrm[s_]:=If[Min@@s==1, mnrm[DeleteCases[s-1, 0]]+1, 0];
Table[Position[q, k][[1, 1]], {k, 2, mnrm[q/.(0->1)]}] (* Gus Wiseman, Feb 20 2025 *)

Prog

(PARI) sopfr(n) = my(f=factor(n)); sum(j=1, #f~, f[j, 1]*f[j, 2]);
sopf(n) = my(f=factor(n)); sum(j=1, #f~, f[j, 1]);
a(n) = {my(k = 2); while (sopfr(k) - sopf(k) != n, k++); k; }

Crossrefs

Cf. A001414 (sopfr), A008472 (sopf), A001248, A280163.

A multiplicative version is A064549 (sorted A001694), firsts of A003557.

For length instead of sum we have A151821.

These are the positions of first appearances in A280292 = A001414 - A008472.

For indices instead of factors we have A380956 (sorted A380957), firsts of A380955.

A multiplicative version for indices is A380987 (sorted A380988), firsts of A290106.

For prime exponents instead of factors we have A380989, firsts of A380958.

The sorted version is A381075.

For product instead of sum see A381076, sorted firsts of A066503.

A000040 lists the primes, differences A001223.

A005117 lists squarefree numbers, complement A013929.

A020639 gives least prime factor (index A055396), greatest A061395 (index A006530).

A056239 adds up prime indices, row sums of A112798.

Cf. A000720, A001222, A046660, A071625, A075255, A116861, A136565, A156061, A178503, A175508, A364916, A366528.

Sequence in context: A118585 A067666 A355012 * A268597 A373319 A253560

Adjacent sequences: A280283 A280284 A280285 * A280287 A280288 A280289

Keyword

nonn

Author

Michel Marcus, Dec 31 2016

Status

approved