A324535 An analog of sigma(n)-n (A001065) for nonstandard factorization based on the sieve of Eratosthenes (A083221).

0, 1, 1, 3, 1, 6, 1, 7, 4, 8, 1, 16, 1, 10, 9, 15, 1, 21, 1, 22, 13, 14, 1, 36, 6, 16, 11, 28, 1, 42, 1, 31, 33, 20, 13, 55, 1, 22, 15, 50, 1, 66, 1, 40, 40, 26, 1, 76, 8, 43, 49, 46, 1, 54, 31, 64, 41, 32, 1, 108, 1, 34, 17, 63, 17, 144, 1, 58, 105, 74, 1, 123, 1, 40, 21, 64, 19, 78, 1, 106, 57, 44, 1, 172, 73, 46, 87, 92, 1, 201, 57, 76, 121

Offset

1,4

Links

Antti Karttunen, Table of n, a(n) for n = 1..16384

Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537

Index entries for sequences generated by sieves

Index entries for sequences related to sigma(n)

Formula

a(n) = A001065(A250246(n)) = A324545(n) - A250246(n).

a(n) = A250246(n) - A324546(n).

Prog

(PARI)
up_to = 65537;
ordinal_transform(invec) = { my(om = Map(), outvec = vector(length(invec)), pt); for(i=1, length(invec), if(mapisdefined(om, invec[i]), pt = mapget(om, invec[i]), pt = 0); outvec[i] = (1+pt); mapput(om, invec[i], (1+pt))); outvec; };
A020639(n) = if(n>1, if(n>n=factor(n, 0)[1, 1], n, factor(n)[1, 1]), 1); \\ From A020639
A055396(n) = if(1==n, 0, primepi(A020639(n)));
v078898 = ordinal_transform(vector(up_to, n, A020639(n)));
A078898(n) = v078898[n];
A003961(n) = my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); \\ From A003961
A250246(n) = if(1==n, n, my(k = 2*A250246(A078898(n)), r = A055396(n)); if(1==r, k, while(r>1, k = A003961(k); r--); (k)));
A001065(n) = (sigma(n)-n);
A324535(n) = A001065(A250246(n));

Crossrefs

Cf. A001065, A250246, A324545, A324546.

Sequence in context: A364858 A001065 A173455 * A318501 A318325 A300244

Adjacent sequences: A324532 A324533 A324534 * A324536 A324537 A324538

Keyword

nonn

Author

Antti Karttunen, Mar 08 2019

Status

approved